Friedrich Schlogl. Probability and Heat
|
|
- Hilda Carr
- 5 years ago
- Views:
Transcription
1 Friedrich Schlogl Probability and Heat
2 Friedrich Schlogl Probability and Heat Fundamentals of Thermostatistics With 52 Figures Springer Fachmedien Wiesbaden GmbH
3 AJlrjghtsreserved Springer Fachmedien Wiesbaden 1989 Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbh, Braunschweig in 1989 Softcover reprint of the hardcover 1 st edition 1989 No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical photocopying or otherwise, without prior permission of the copyrjght holder. Set by Vieweg, Braunschwejg Bound by W. Langeltiddecke, Braunschwejg ISBN ISBN (ebook) DOI /
4 v Contents Preface and Introduction IX How to Read this Book XII 1 General Statistics Probability Events Definitions of Probability Random Quantities Moments and Cumulants The Normal Distribution * The Central Limit Theorem lnfonnation Measures Shannon Information Information Gain * Stochastic Matrices Generalized Canonical DistnlJUtions The Unbiased Guess Properties of the Generalized Canonical distribution Addition of Knowledge Thermodynamics of Equilibria Thennal States Direction of Time The Liouville Theorem Equilibrium Distributions *2.1.4 Statistical Operators in Quantum Mechanics *2.1.5 The Wigner Function... : Thermal Variables Statistical Foundations of the Macroscopic Scheme The Second Law of Thermodynamics Work and Heat Standard Distributions Extensities as Sharp Parameters The Carnot Cycle * By an asterisc are designated parts of more special interest. They can be skipped by the reader without lost of continuity.
5 VI Contents 2.3 The Phenomenological Framework The Basic Laws of Thermodynamics Definition of Absolute Temperature Entropy in Phenomenology Thermodynamic Potentials Thermal and Caloric Equations of State Availability Equilibrium Conditions Stability Relations Specific Heat The Low Temperature Regime The Nernst Theorem Characteristic Quantities at Zero Point Unattainability of Absolute Zero Point *2.4.4 Reactions at Low Temperature Macroscopic Description of Special Systems Gases and Solutions Ideal Gases and Dilute Solutions MixturesofldealGases Ideal Mixtures Real Gases Chemical Reactions Reaction Heat Chemical Affinity The Law of Mass Action Electro-Chemical Potentials The Method of Cycle Processes An Isothermal Cycle Vapor Pressure and Radiation Cavity Microscopic Description of Special Systems Thermal Equations of State Ideal Gas Grand Canonical Ensemble Real Gases *4.1.4 Cell Model of a Liquid Perfect Bose and Fermi Gas The Radiation Cavity * By an asterisc are designated parts of more special interest. They can be skipped by the reader without lost of continuity.
6 Contents VII 4.2 Specific Heat Specific Heat ofldea1 Gases Ortho- and Para-Hydrogen Specific Heat of Solids Magnetism Paramagnetism Weiss Theory of Ferromagnetism *4.3.3 The/singModel *4.3.4 The Long Range Order *4.3.5 Bethe-Peierls Approximation N onequilibria Thermal Fluctuations Fluctuations and Susceptibilities Probability of Fluctuations Applications of Einstein's Fluctuation Formula *5.1.4 Maxwell's Demon Nonequilibrium Dynamics * The Liouville Operator TheMori Distribution *5.2.3 The Wangsness-Bloch Equation *5.2.4 Thermodynamic Uncertainty Relation Linear Thermodynamics Fluxes and Forces Onsager Symmetry Entropy Production Heat Conduction Thermodiffusion The Einstein Relation of Diffusion *5.3.7 Einstein's Deduction of Planck's Radiation Formula *5.4 A Model of Time Scale Separation *5.4.1 Autocorrelations in the Harmonic Chain *5.4.2 Causal Functions *5.4.3 The Macroscopic Motion Index * By an asterisc are designated parts of more special interest. They can be skipped by the reader without lost of continuity.
7 IX Preface and Introduction This book is based on lectures for graduate students of physics and physical chemistry. Its main aim is to represent the connections between the microdynamics of molecules and quanta with the macroscopic thermodynamics. There are many excellent textbooks on thermodynamics, and the question arises why another one should be written. In no other field of physics we can find as many different possible ways of introducing the theory as in thermodynamics. The reason is not only that here we have to distinguish between a macroscopic and a microscopic description of the same phenomena. The concept of probability in the statistical theory of thermodynamics introduces a fundamentally new element into physics. Between experience and the conventional theories, the use of probability was an intermediate new methodical element which did not occur in the fundamentals of classical physics before the development of thermodynamics. Originally, probability was not used in pure macroscopic thermodynamics, which had developed independently into a rather closed theory based on its own set of postulates. After further development, however, it became possible to connect these postulates with other fields of physics by deducing thermodynamics from statistical mechanics. As a result of this connection it is not surprising that macroscopic thermodynamics is less concrete and less transparent than other fields of classical physics, notwithstanding that, as a rule, understanding it does not require difficult calculus. Such notions as "entropy", "enthalpy", and their relatives, are more abstract and less directly connected with experience or pictures than most of the basic notions in other fields. Even the restriction that we can apply the rather elementary notion "temperature" only to certain kinds of states of a system, does not support the belief that, apart from the subtelities of time averaging, existence of equilibrium, and other conditions required for its definition, temperature is one of the simplest concepts in physics. Only because temperature is associated with a sensual perception, we accept it as familiar to us. The use of probability in physics requires certain methodological assumptions which, strictly speaking, are not based on experience, but which are necessary to organize experience. As in most cases in which such assumptions are introduced into thermodynamics without clear separation from empirical elements, they are often associated with conceptual difficulties. A central aim of this book is to overcome these difficulties in a specific way. The book strives for a clear separation of the physical fundamentals of thermodynamics from the general stochastic fundamentals, which in principle do not need to be restricted to their application in physics. This procedure, in a consistent way, is different from that of the usual procedure of textbooks on thermodynamics. It is chosen only because the author believes that it makes things simpler and more transparent in statistical thermodynamics. Indeed, many well-known basic relations of thermodynamics will turn out to be results already of the general stochastic theory. This is the reason for extensive analogies to thermodynamic concepts and connections occurring in modern theories of computer simulation of physical and nonphysical processes. We shall not deal with this field in this book. The above mentioned systematic separation of the different fundamentals, however, will also be useful for understanding the origin of these analogies.
8 X Preface and Introduction The general stochastic fundamentals comprise more than the mathematical aspects of probability theory. They also include methods of applying probability theory to experience in an appropriate way. Therefore, in the first section of this book, which is devoted to the stochastic fundamentals, we shall also be concerned with elements of information theory. The main objective of this book is to analyse the connection between thermodynamics and the dynamics on the level of the most detailed description, in the "phase space". Statistics as the foundation of thermodynamics is here understood to be statistics over microstates in phase space. This topical restriction implies that generally we shall not use statistics on a "mesoscopic" level as an ad hoc assumption and as a starting point in its own rights. Due to this restriction of the book we shall not be concerned with the Boltzmann collision equation, with the master equation, with Langevin forces, or with stochastic processes, albeit these methods have proved to be very successful in nonequilibrium thermodynamics. There we refer to expositions existing in the rich literature on the statistical theory of nonequilibrium processes. Mesoscopic statistics will occur only as result of the basic statistics over the microstates. Another restriction is that we consider nonequilibrium processes only if they occur in the regime of "linear thermodynamics". Hence we shall not include the steadily expanding field of modern research of "nonlinear thermodynamics" because this would lead too far. Although the major concern of the book is the foundation of thermodynamics on the statistical theory, the macroscopic theory will not be represented only as result of the statistics. The macroscopic theory will be developed once again and independently within the pure macroscopic, phenomenological framework. This is done because this framework is an impressive, logically closed system which can be understood without complicated mathematics. The macroscopic theory is moreover a very useful tool for applications which can also be handled without knowledge of the statistical theory. It should be stressed that the simplicity aspired to in the representation of the basic postulates of the phenomenological thermodynamics is not primarily that of logical economy with respect to the independence of basic axioms. It is rather the simplicity of an utmost transparent connection of the basic assumptions with experience on the one hand, and with their consequences on the other hand. Thus the book does not compete with representations of the mathematical axiomatics of phenomenological thermodynamics, which developed into a separate field of research. The book may differ from the conventional representations in textbooks not only in the previously mentioned striving for a clear separation of methodical from empirical elements but also in other points. This is the case, for instance, with the interpretation of specific heat as statistical measure in chapter , together with the chapters 5.1.2, and Another point may be the accent placed on the significance of "information gain" and its correlates "availability" and "produced entropy" in thermodynamics. These concepts elucidate some connections more clearly and at times allow for shorter deductions. In the last subsection 5.4, which has rather the character of an appendix, a model system is discussed which at first sight may look a bit far afield from the primary theme of this book. Nevertheless, this subsection deals with two central questions in thermodynamics. The first one is how a mechanical system with reversible dynamics on the microscopic level can exhibit irreversible macroscopic dynamics. The second question is how the motion of such a system can develop a distinctive time scale separation between microscopic and macroscopic processes. These questions cannot be answered analytically in a general way. For the considered model, however, a rigorous solution of these problems is possible.
9 Preface and Introduction XI The book is meant to be primarily a textbook. Therefore most of the examples of special thermodynamic systems are standards in different fields. The number of the examples, however, is restricted. For more applications we refer the reader to the rich literature on thermodynamics. The author hopes that the book, which is concerned above all with basic connections, will be interesting not only for students but also for academic teachers and other scientists who like the structural analysis of fundamentals in physics. According to the character of a textbook, this book is not intended to demonstrate new results. Nevertheless, the way of the logical deductions, and of the presentations used in this book, as well as the choice of illustrating examples are not only influenced by literature but also by discussions with colleagues and friends. In this respect I should like to mention the Professors A. Stahl, J. Meixner, R. Bausch, H.-K. Janssen, R. Bessenrodt, Dr. E. Scholl, and Dr. C. Escher in Germany, as well as Professor C. A. Mead in Minneapolis, and Professor R. St. Berry in Chicago. Particular thank is directed to Professor V. Dohm for critically reading certain parts of the manuscript and making valuable proposals for improvements. Above all I should like to mention my unforgettable late academic teacher Professor Richard Becker in Gottingen, who, now half a century ago, first raised my love for this field. I gratefully acknowledge the help of my niece Dr. Aenne Hannon, Houston, Texas, in reducing the linguistic shortcomings of the manuscript I had written in a language which is not my native tongue. Last but not least, I want to thank the publisher, whose suggestion and interest made this book possible. Aachen, December 1988 Friedrich Schlag!
10 XII How to Read this Book The book is divided into main sections designated by only one serial number, into subsections designated by two numbers, and into chapters designated by three numbers. The first number always marks the main section, the second the subsection, and the third the chapter. Within a subsection, the equations are designated by two numbers, the first corresponding to the chapter, the second to the equation itself. Footnotes and figures are designated by serial numbers running continuously through the whole book. The reader who is familiar with probability theory may skip subsection 1.1 and use this part only for occasional reference. The same is true with respect to information theory for subsection 1.2. Subsection 1.3, however, is essential for the whole structure of the book because, even at an early stage, it presents important basic relations of thermodynamics which are results of a general statistical theory, independent of underlying physics. Several chapters and parts of chapters, in particular those which require more advanced knowledge, for instance of quantum mechanics, may be skipped without loss of the logical continuity, both by beginners and by the reader who is mainly interested in the practical application of thermodynamics. These parts are marked by an asterisk in the title. The already mentioned subsection 5.4 is actually an appendix for specially interested readers. Subsection 2.3 does not rely on the statistical theory, with the exception of some additional excursions which are made and are obvious as such. This part of the book should be readable without knowledge of all the other parts and the author hopes that it can be helpful also for a reader who is only interested in macroscopic thermodynamics. References with respect to special literature are made in footnotes. They are made only if the subject is not considered to be of textbook standard.
Statistical Mechanics
Franz Schwabl Statistical Mechanics Translated by William Brewer Second Edition With 202 Figures, 26 Tables, and 195 Problems 4u Springer Table of Contents 1. Basic Principles 1 1.1 Introduction 1 1.2
More informationTHERMODYNAMICS THERMOSTATISTICS AND AN INTRODUCTION TO SECOND EDITION. University of Pennsylvania
THERMODYNAMICS AND AN INTRODUCTION TO THERMOSTATISTICS SECOND EDITION HERBERT B. University of Pennsylvania CALLEN JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore CONTENTS PART I GENERAL
More informationPH4211 Statistical Mechanics Brian Cowan
PH4211 Statistical Mechanics Brian Cowan Contents 1 The Methodology of Statistical Mechanics 1.1 Terminology and Methodology 1.1.1 Approaches to the subject 1.1.2 Description of states 1.1.3 Extensivity
More informationINTRODUCTION TO MODERN THERMODYNAMICS
INTRODUCTION TO MODERN THERMODYNAMICS Dilip Kondepudi Thurman D Kitchin Professor of Chemistry Wake Forest University John Wiley & Sons, Ltd CONTENTS Preface xiii PART I THE FORMALIS1VI OF MODERN THER1VIODYNAMICS
More informationThermal Plasmas. Fundamentals and Applications. Volume 1
Thermal Plasmas Fundamentals and Applications Volume 1 Thermal Plasmas Fundamentals and Applications Volume 1 Maher I. Boulos University 0/ Sherbrooke Sherbrooke, Quebec, Canada Pierre Fauchais University
More informationContents. 1 Introduction and guide for this text 1. 2 Equilibrium and entropy 6. 3 Energy and how the microscopic world works 21
Preface Reference tables Table A Counting and combinatorics formulae Table B Useful integrals, expansions, and approximations Table C Extensive thermodynamic potentials Table D Intensive per-particle thermodynamic
More informationSuggestions for Further Reading
Contents Preface viii 1 From Microscopic to Macroscopic Behavior 1 1.1 Introduction........................................ 1 1.2 Some Qualitative Observations............................. 2 1.3 Doing
More informationThermodynamics, Gibbs Method and Statistical Physics of Electron Gases
Bahram M. Askerov Sophia R. Figarova Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases With im Figures Springer Contents 1 Basic Concepts of Thermodynamics and Statistical Physics...
More informationProbability Theory, Random Processes and Mathematical Statistics
Probability Theory, Random Processes and Mathematical Statistics Mathematics and Its Applications Managing Editor: M.HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume
More informationFundamentals. Statistical. and. thermal physics. McGRAW-HILL BOOK COMPANY. F. REIF Professor of Physics Universüy of California, Berkeley
Fundamentals of and Statistical thermal physics F. REIF Professor of Physics Universüy of California, Berkeley McGRAW-HILL BOOK COMPANY Auckland Bogota Guatemala Hamburg Lisbon London Madrid Mexico New
More informationElementary Lectures in Statistical Mechanics
George DJ. Phillies Elementary Lectures in Statistical Mechanics With 51 Illustrations Springer Contents Preface References v vii I Fundamentals: Separable Classical Systems 1 Lecture 1. Introduction 3
More informationPHY 6500 Thermal and Statistical Physics - Fall 2017
PHY 6500 Thermal and Statistical Physics - Fall 2017 Time: M, F 12:30 PM 2:10 PM. From 08/30/17 to 12/19/17 Place: Room 185 Physics Research Building Lecturer: Boris Nadgorny E-mail: nadgorny@physics.wayne.edu
More informationTHERMAl PHYSICS. P. C. RIEDl AN INTRODUCTION TO THERMODYNAMICS, STATISTICAL MECHANICS AND KINETIC THEORY
THERMAL PHYSICS THERMAl PHYSICS AN INTRODUCTION TO THERMODYNAMICS, STATISTICAL MECHANICS AND KINETIC THEORY P. C. RIEDl Department of Phsyics, University of St Andrews M P. C. Riedi 1976 Softcover reprint
More informationINTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition
INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition Kerson Huang CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an Informa
More informationTime-Dependent Statistical Mechanics 1. Introduction
Time-Dependent Statistical Mechanics 1. Introduction c Hans C. Andersen Announcements September 24, 2009 Lecture 1 9/22/09 1 Topics of concern in the course We shall be concerned with the time dependent
More informationA Macmillan Physics Text
WAVES A Macmillan Physics Text Consulting Editor: Professor P. A. Matthews, F.R.S. Other titles MODERN ATOMIC PHYSICS: FUNDAMENTAL PRINCIPLES: B. Cagnacand J. -C. Pebay-Peyroula MODERN ATOMIC PHYSICS:
More informationSyllabus and Topics Thermal Physics I Fall 2007
Syllabus and Topics 33-341 Thermal Physics I Fall 2007 Robert F. Sekerka 6416 Wean Hall, Phone 412-268-2362 sekerka@cmu.edu http://sekerkaweb.phys.cmu.edu August 27, 2007 Class Schedule: This class is
More informationFISES - Statistical Physics
Coordinating unit: 230 - ETSETB - Barcelona School of Telecommunications Engineering Teaching unit: 748 - FIS - Department of Physics Academic year: Degree: 2018 BACHELOR'S DEGREE IN ENGINEERING PHYSICS
More informationSyllabus and Topics Statistical Mechanics Thermal Physics II Spring 2009
Syllabus and Topics 33-765 Statistical Mechanics 33-342 Thermal Physics II Spring 2009 Robert F. Sekerka 6416 Wean Hall, Phone 412-268-2362 rs07@andrew.cmu.edu http://sekerkaweb.phys.cmu.edu January 12,
More informationChapter 1. Introduction
Chapter 1 Introduction Thermodynamics in the generalized sense is a branch of natural science in which we study heat, work, energy, their interrelationships, and the modes by which systems exchange heat,
More informationfiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
Content-Thermodynamics & Statistical Mechanics 1. Kinetic theory of gases..(1-13) 1.1 Basic assumption of kinetic theory 1.1.1 Pressure exerted by a gas 1.2 Gas Law for Ideal gases: 1.2.1 Boyle s Law 1.2.2
More informationElectrical Transport in Nanoscale Systems
Electrical Transport in Nanoscale Systems Description This book provides an in-depth description of transport phenomena relevant to systems of nanoscale dimensions. The different viewpoints and theoretical
More informationShigeji Fujita and Salvador V Godoy. Mathematical Physics WILEY- VCH. WILEY-VCH Verlag GmbH & Co. KGaA
Shigeji Fujita and Salvador V Godoy Mathematical Physics WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XIII Table of Contents and Categories XV Constants, Signs, Symbols, and General Remarks
More informationReliability Evaluation of Engineering Systems:
Reliability Evaluation of Engineering Systems: Concepts and Techniques Roy Billinton PhD, DSc, FEIC, FRSC, FIEEE, PE c. J. MacKenzie Professor of Electrical Engineering University of Saskatchewan and Ronald
More informationThermal Physics. Energy and Entropy
Thermal Physics Energy and Entropy Written by distinguished physics educator, this fresh introduction to thermodynamics, statistical mechanics and the study of matter is ideal for undergraduate courses.
More informationNPTEL
NPTEL Syllabus Nonequilibrium Statistical Mechanics - Video course COURSE OUTLINE Thermal fluctuations, Langevin dynamics, Brownian motion and diffusion, Fokker-Planck equations, linear response theory,
More informationNON-EQUILIBRIUM THERMODYNAMICS
NON-EQUILIBRIUM THERMODYNAMICS S. R. DE GROOT Professor of Theoretical Physics University of Amsterdam, The Netherlands E MAZUR Professor of Theoretical Physics University of Leiden, The Netherlands DOVER
More informationTable of Contents [ttc]
Table of Contents [ttc] 1. Equilibrium Thermodynamics I: Introduction Thermodynamics overview. [tln2] Preliminary list of state variables. [tln1] Physical constants. [tsl47] Equations of state. [tln78]
More informationNumerical Data Fitting in Dynamical Systems
Numerical Data Fitting in Dynamical Systems Applied Optimization Volume 77 Series Editors: Panos M. Pardalos University of Florida, U.S.A. Donald Hearn University of Florida, U.S.A. The titles published
More informationHEAT AND THERMODYNAMICS PHY 522 Fall, 2010
HEAT AND THERMODYNAMICS PHY 522 Fall, 2010 I. INSTRUCTOR Professor Lance De Long Office: CP363 (257-4775) Labs: CP75, CP158 (257-8883), ASTeCC A041 Office Hours: M 10:30-11:30 a.m.; T 8:30-9:30 a.m. II.
More informationTHEORY OF MOLECULAR EXCITONS
THEORY OF MOLECULAR EXCITONS THEORY OF MOLECULAR EXCITONS A. S. Davydov Kiev State University Kiev, USSR Translated from Russian by Stephen B. Dresner g? SPRINGER SCIENCE+BUSINESS MEDIA, LLC 1971 Aleksandr
More informationFUNDAMENTALS OF CHEMISTRY Vol. II - Irreversible Processes: Phenomenological and Statistical Approach - Carlo Cercignani
IRREVERSIBLE PROCESSES: PHENOMENOLOGICAL AND STATISTICAL APPROACH Carlo Dipartimento di Matematica, Politecnico di Milano, Milano, Italy Keywords: Kinetic theory, thermodynamics, Boltzmann equation, Macroscopic
More informationCircuit Analysis for Power Engineering Handbook
Circuit Analysis for Power Engineering Handbook Circuit Analysis for Power Engineering Handbook Arieh L. Shenkman SPRINGER SCIENCE+BUSINESS MEDIA, B.V A c.i.p. Catalogue record for this book is available
More informationSyllabus and Topics Statistical Mechanics Spring 2011
Syllabus and Topics 33-765 Statistical Mechanics Spring 2011 Robert F. Sekerka 6416 Wean Hall, Phone 412-268-2362 rs07@andrew.cmu.edu http://sekerkaweb.phys.cmu.edu January 10, 2011 Course and Credit:
More information1. Thermodynamics 1.1. A macroscopic view of matter
1. Thermodynamics 1.1. A macroscopic view of matter Intensive: independent of the amount of substance, e.g. temperature,pressure. Extensive: depends on the amount of substance, e.g. internal energy, enthalpy.
More informationMASTER OF SCIENCE IN PHYSICS
MASTER OF SCIENCE IN PHYSICS The Master of Science in Physics program aims to develop competent manpower to fill the demands of industry and academe. At the end of the program, the students should have
More informationThermodynamics. 1.1 Introduction. Thermodynamics is a phenomenological description of properties of macroscopic systems in thermal equilibrium.
1 hermodynamics 1.1 Introduction hermodynamics is a phenomenological description of properties of macroscopic systems in thermal equilibrium. Imagine yourself as a post-newtonian physicist intent on understanding
More informationHari Dass, N.D. The principles of thermodynamics digitalisiert durch: IDS Basel Bern
Hari Dass, N.D. The principles of thermodynamics 2014 digitalisiert durch: IDS Basel Bern Preface Guide for readers and teachers xiii xv Chapter 1 The Beginnings 1 1.1 Temperature and 2 1.1.1 Uniform temperature
More informationTRANSPORT PHENOMENA AND UNIT OPERATIONS
TRANSPORT PHENOMENA AND UNIT OPERATIONS TRANSPORT PHENOMENA AND UNIT OPERATIONS A COMBINED APPROACH Richard G. Griskey A JOHN WILEY & SONS, INC., PUBLICATION This book is printed on acid-free paper Copyright
More informationAN INTRODUCTION TO HYDRODYNAMICS AND WATER WAVES
AN INTRODUCTION TO HYDRODYNAMICS AND WATER WAVES HYDRODYNAMICA SIVE DE VIRIBUS ET MOTIBUS FLUIDORUM COMMENTARII 'Remember, when discoursing about water, to induce first experience, then reason.' - Leonardo
More informationRarefied Gas Dynamics
Rarefied Gas Dynamics Rarefied Gas Dynamics Mikhail N. Kogan Computer Center Academy of Sciences of the USSR Moscow Translated from Russian Translation Editor Leon Trilling Department of Aeronautics and
More informationChemistry by Computer. An Overview of the Applications of Computers in Chemistry
Chemistry by Computer An Overview of the Applications of Computers in Chemistry Chemistry by Computer An Overview of the Applications of Computers in Chemistry Stephen Wilson Theoretical Chemistry Department
More informationTime-Dependent Statistical Mechanics 5. The classical atomic fluid, classical mechanics, and classical equilibrium statistical mechanics
Time-Dependent Statistical Mechanics 5. The classical atomic fluid, classical mechanics, and classical equilibrium statistical mechanics c Hans C. Andersen October 1, 2009 While we know that in principle
More informationThe Boltzmann Equation and Its Applications
Carlo Cercignani The Boltzmann Equation and Its Applications With 42 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo CONTENTS PREFACE vii I. BASIC PRINCIPLES OF THE KINETIC
More informationEK 04: Energy and Thermodynamics Lectures Professor i Lin Course Page: http://oned.bu.edu/ek04 Email: linx@bu.edu; Phone: (67) 58-47 Textbook Lecture Notes and Problem Sets Fundamental of Engineering Thermodynamics
More informationStatistical Mechanics
Statistical Mechanics Entropy, Order Parameters, and Complexity James P. Sethna Laboratory of Atomic and Solid State Physics Cornell University, Ithaca, NY OXFORD UNIVERSITY PRESS Contents List of figures
More informationCollection of problems in probability theory
Collection of problems in probability theory L. D. MESHALKIN Moscow State University Collection of problems in probability theory Translated from the Russian and edited by LEO F. BORON University of Idaho
More informationNanoscale Energy Transport and Conversion A Parallel Treatment of Electrons, Molecules, Phonons, and Photons
Nanoscale Energy Transport and Conversion A Parallel Treatment of Electrons, Molecules, Phonons, and Photons Gang Chen Massachusetts Institute of Technology OXFORD UNIVERSITY PRESS 2005 Contents Foreword,
More informationInitial Boundary Value Problems in Mathematical Physics
Initial Boundary Value Problems in Mathematical Physics Initial Boundary Value Problems in Mathematical Physics Rolf leis University of Bonn Federal Republic of Germany Springer Fachmedien Wiesbaden GmbH
More informationPHYSICS 715 COURSE NOTES WEEK 1
PHYSICS 715 COURSE NOTES WEEK 1 1 Thermodynamics 1.1 Introduction When we start to study physics, we learn about particle motion. First one particle, then two. It is dismaying to learn that the motion
More informationSyllabus and Topics Statistical Mechanics Spring 2010
Syllabus and Topics 33-765 Statistical Mechanics Spring 2010 Robert F. Sekerka 6416 Wean Hall, Phone 412-268-2362 rs07@andrew.cmu.edu http://sekerkaweb.phys.cmu.edu January 10, 2010 Course and Credit:
More informationElectrochemical Process Engineering. A Guide to the Design of Electrolytic Plant
Electrochemical Process Engineering A Guide to the Design of Electrolytic Plant Electrochemical Process Engineering A Guide to the Design of Electrolytic Plant F. Goodridge and K. Scott University of Newcastle
More informationDEPARTMENT OF PHYSICS
Department of Physics 1 DEPARTMENT OF PHYSICS Office in Engineering Building, Room 124 (970) 491-6206 physics.colostate.edu (http://www.physics.colostate.edu) Professor Jacob Roberts, Chair Undergraduate
More informationChapter 1. Introduction
Chapter 1 Introduction The book Introduction to Modern Physics: Theoretical Foundations starts with the following two paragraphs [Walecka (2008)]: At the end of the 19th century, one could take pride in
More informationChem 350: Statistical Mechanics and Chemical Kinetics. Spring Preface. Introduction 2
Preface Introduction 2 Statistical Mechanics and Chemical Kinetics: Syllabus Textbook: Thermodynamics, Statistical Thermodynamics and Kinetics 3 rd ed by Thomas Engel and Philip Reid Additional Resource
More informationPhysics and Astronomy
Statistical Mechanics Springer-Verlag Berlin Heidelberg GmbH Physics and Astronomy ONLINE LIBRARY http://www.springer.de/phys/ Advanced Texts in Physics This program of advanced texts covers a broad spectrum
More informationPhysics 112 Spring 2014
Physics 112 Spring 2014 Phys 112 (S12) Syllabus/introduction 1 Goals Deeper understanding of concepts: less mysterious Entropy Free energy Chemical potential Statistical mechanics fluctuations kinetic
More informationStatistical Mechanics
42 My God, He Plays Dice! Statistical Mechanics Statistical Mechanics 43 Statistical Mechanics Statistical mechanics and thermodynamics are nineteenthcentury classical physics, but they contain the seeds
More informationChemistry Physical Chemistry I Fall 2018
Chemistry 309 - Physical Chemistry I Fall 2018 Instructor: Office Hours: Dr. Samuel A. Abrash C-208 Gottwald Science Center Work: 289-8248 Home: 323-7363 Cell: 363-2597 sabrash@richmond.edu www.richmond.edu/~sabrash
More informationBASIC ENGINEERING MECHANICS
BASIC ENGINEERING MECHANICS Other titles of interest to engineers An Introduction to Engineering Fluid Mechanics J. A. Fox Principles of Engineering Thermodynamics E. M. Goodger Analysis and Presentation
More informationTopics for the Qualifying Examination
Topics for the Qualifying Examination Quantum Mechanics I and II 1. Quantum kinematics and dynamics 1.1 Postulates of Quantum Mechanics. 1.2 Configuration space vs. Hilbert space, wave function vs. state
More informationPreface to the Fifth Edition
Preface to the Fifth Edition Since the previous fourth edition has received quite a positive response from students as well as teachers, we have decided to extend the contents and improve some chapters
More informationBachelor s Degree in Chemistry. 1 st YEAR Mechanics and Thermodynamics ECTS credits: 6 Semester: 1. Teaching objectives
1 st YEAR 5263 Mechanics and Thermodynamics ECTS credits: 6 Semester: 1 The student should be able to: 1. Understand the concepts and describe the fundamental aspects of Mechanics and Thermodynamics. 2.
More informationPHYSICAL PROCESSES IN SOLAR FLARES
PHYSICAL PROCESSES IN SOLAR FLARES ASTROPHYSICS AND SPACE SCIENCE LIBRARY A SERIES OF BOOKS ON THE RECENT DEVELOPMENTS OF SPACE SCIENCE AND OF GENERAL GEOPHYSICS AND ASTROPHYSICS PUBLISHED IN CONNECTION
More informationIntroduction. Chapter The Purpose of Statistical Mechanics
Chapter 1 Introduction 1.1 The Purpose of Statistical Mechanics Statistical Mechanics is the mechanics developed to treat a collection of a large number of atoms or particles. Such a collection is, for
More informationIntroduction to Statistical Physics
Introduction to Statistical Physics Rigorous and comprehensive, this textbook introduces undergraduate students to simulation methods in statistical physics. The book covers a number of topics, including
More informationUndergraduate Texts in Mathematics. Editors J. H. Ewing F. W. Gehring P. R. Halmos
Undergraduate Texts in Mathematics Editors J. H. Ewing F. W. Gehring P. R. Halmos Springer Books on Elemeritary Mathematics by Serge Lang MATH! Encounters with High School Students 1985, ISBN 96129-1 The
More informationStudents are required to pass a minimum of 15 AU of PAP courses including the following courses:
School of Physical and Mathematical Sciences Division of Physics and Applied Physics Minor in Physics Curriculum - Minor in Physics Requirements for the Minor: Students are required to pass a minimum of
More informationNANO/MICROSCALE HEAT TRANSFER
NANO/MICROSCALE HEAT TRANSFER Zhuomin M. Zhang Georgia Institute of Technology Atlanta, Georgia New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore
More informationChemistry Physical Chemistry I Fall 2017
Chemistry 309 - Physical Chemistry I Fall 2017 Instructor: Office Hours: Dr. Samuel A. Abrash C208 Gottwald Science Center Work: 289-8248 Home: 323-7363 Cell: 363-2597 sabrash@richmond.edu www.richmond.edu/~sabrash
More informationHeat, Temperature and the First Law of Thermodynamics
Heat, Temperature and the First Law of Thermodynamics Stephen R. Addison January 22, 2003 Introduction The object of our studies is thermal physics. Thermal physics is a combination of two historic disciplines:
More informationPHYSICS-PH (PH) Courses. Physics-PH (PH) 1
Physics-PH (PH) 1 PHYSICS-PH (PH) Courses PH 110 Physics of Everyday Phenomena (GT-SC2) Credits: 3 (3-0-0) Fundamental concepts of physics and elementary quantitative reasoning applied to phenomena in
More informationNonequilibrium Statistical Mechanics
Nonequilibrium Statistical Mechanics Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: Alwyn
More information84 My God, He Plays Dice! Chapter 12. Irreversibility. This chapter on the web informationphilosopher.com/problems/reversibility
84 My God, He Plays Dice! This chapter on the web informationphilosopher.com/problems/reversibility Microscopic In the 1870 s, Ludwig Boltzmann developed his transport equation and his dynamical H-theorem
More informationTheoretical Physics 4
Theoretical Physics 4 Wolfgang Nolting Theoretical Physics 4 Special Theory of Relativity 123 Wolfgang Nolting Inst. Physik Humboldt-UniversitRat zu Berlin Berlin, Germany ISBN 978-3-319-44370-6 ISBN 978-3-319-44371-3
More informationMP203 Statistical and Thermal Physics. Jon-Ivar Skullerud and James Smith
MP203 Statistical and Thermal Physics Jon-Ivar Skullerud and James Smith October 3, 2017 1 Contents 1 Introduction 3 1.1 Temperature and thermal equilibrium.................... 4 1.1.1 The zeroth law of
More informationMASTER OF PHYSICS. iii.) Compliance of the School of Graduate Studies and the Institute admission requirements.
MASTER OF PHYSICS Rationale Consistent with the mandate of the Commission of Higher Education (CHED) as Center-of-Excellence (COE) of Physics outside of Luzon and as a DOST-PCASTRD accredited institution
More informationnon equilibrium thermodynamics and the production of entropy life earth and beyond understanding complex systems
DOWNLOAD OR READ : NON EQUILIBRIUM THERMODYNAMICS AND THE PRODUCTION OF ENTROPY LIFE EARTH AND BEYOND UNDERSTANDING COMPLEX SYSTEMS PDF EBOOK EPUB MOBI Page 1 Page 2 non equilibrium thermodynamics and
More informationSyllabus for CH-3300 Introduction to Physical Chemistry
Syllabus for CH-3300 Introduction to Physical Chemistry Overview: This class will introduce concepts of physical chemistry particularly relevant to the medicinal and life sciences. While developing the
More informationQUANTUM MECHANICS. For Electrical Engineers. Quantum Mechanics Downloaded from
Quantum Mechanics Downloaded from www.worldscientific.com QUANTUM MECHANICS For Electrical Engineers Quantum Mechanics Downloaded from www.worldscientific.com This page intentionally left blank Quantum
More informationHugh Everett III s Many Worlds
236 My God, He Plays Dice! Hugh Everett III s Many Worlds Many Worlds 237 Hugh Everett III s Many Worlds Hugh Everett III was one of John Wheeler s most famous graduate students. Others included Richard
More informationTHEORY OF PLASMAS TEORIYA PLAZMY. TEOPMH lljla3mbi
THEORY OF PLASMAS TEORIYA PLAZMY TEOPMH lljla3mbi The Lebedev Physics Institute Series Editors: Academicians D. V. Skobel'tsyn and N. G. Basov P. N. Lebedev Physics Institute, Academy of Sciences of the
More informationProcedure for Setting Goals for an Introductory Physics Class
Procedure for Setting Goals for an Introductory Physics Class Pat Heller, Ken Heller, Vince Kuo University of Minnesota Important Contributions from Tom Foster, Francis Lawrenz Details at http://groups.physics.umn.edu/physed
More informationThe Oxford Solid State Basics
The Oxford Solid State Basics Steven H. Simon University of Oxford OXFORD UNIVERSITY PRESS Contents 1 About Condensed Matter Physics 1 1.1 What Is Condensed Matter Physics 1 1.2 Why Do We Study Condensed
More informationMolecular Aggregation
Molecular Aggregation Structure Analysis and Molecular Simulation of Crystals and Liquids ANGELO GAVEZZOTTI University of Milano OXFORD UNIVERSITY PRESS Contents PART I FUNDAMENTALS 1 The molecule: structure,
More informationGraduate Texts in Mathematics 22
Graduate Texts in Mathematics 22 Managing Editors: P. R. Halmos C. C. Moore Donald W. Barnes lohn M. Mack An Aigebraic Introduction to Mathematical Logic Springer Science+Business Media, LLC Donald W.
More informationTable of Contents Preface PART I. MATHEMATICS
Table of Contents Preface... v List of Recipes (Algorithms and Heuristics)... xi PART I. MATHEMATICS... 1 Chapter 1. The Game... 3 1.1 Systematic Problem Solving... 3 1.2 Artificial Intelligence and the
More informationSecond law, entropy production, and reversibility in thermodynamics of information
Second law, entropy production, and reversibility in thermodynamics of information Takahiro Sagawa arxiv:1712.06858v1 [cond-mat.stat-mech] 19 Dec 2017 Abstract We present a pedagogical review of the fundamental
More informationChapter 2 Ensemble Theory in Statistical Physics: Free Energy Potential
Chapter Ensemble Theory in Statistical Physics: Free Energy Potential Abstract In this chapter, we discuss the basic formalism of statistical physics Also, we consider in detail the concept of the free
More informationCollective behavior, from particles to fields
978-0-51-87341-3 - Statistical Physics of Fields 1 Collective behavior, from particles to fields 1.1 Introduction One of the most successful aspects of physics in the twentieth century was revealing the
More informationRudolf Taschner. The Continuum
Rudolf Taschner The Continuum Rudolf Taschner The Continuum A Constructive Approach to Basic Concepts of Real Analysis ai vleweg Bibliographic information published by Die Deutsche Bibliothek Die Deutsche
More informationList of Comprehensive Exams Topics
List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle
More informationSTOCHASTIC PROCESSES FOR PHYSICISTS. Understanding Noisy Systems
STOCHASTIC PROCESSES FOR PHYSICISTS Understanding Noisy Systems Stochastic processes are an essential part of numerous branches of physics, as well as biology, chemistry, and finance. This textbook provides
More informationRaymond Gerard Hidetoshi Tahara. Singular Nonlinear Partial Differential Equations
Raymond Gerard Hidetoshi Tahara Singular Nonlinear Partial Differential Equations Aspects Mathematics Edited by Klas Diederich Vol. E 3: Vol. E 5: Vol. E 6: Vol. E 7: Vol. E 9: Vol. E 10: G. Hector/U.
More informationpka Prediction for Organic Acids and Bases
pka Prediction for Organic Acids and Bases pka Prediction for Organic Acids and Bases D. D. Perrin John Curtin School of Medical Research Australian National Universi~oy Canberra Boyd Dempsey and E. P.
More informationTERMO - Thermodynamics
Coordinating unit: 230 - ETSETB - Barcelona School of Telecommunications Engineering Teaching unit: 748 - FIS - Department of Physics Academic year: Degree: 2018 BACHELOR'S DEGREE IN ENGINEERING PHYSICS
More informationAnalysis and Control of Age-Dependent Population Dynamics
Analysis and Control of Age-Dependent Population Dynamics MATHEMATICAL MODELLING: Theory and Applications VOLUME I I This series is aimed at publishing work dealing with the definition, development and
More informationINTRODUCTION TO SOL-GEL PROCESSING
INTRODUCTION TO SOL-GEL PROCESSING THE KLUWER INTERNATIONAL SERIES in SOL-GEL PROCESSING: TECHNOLOGY AND APPLICATIONS Consulting Editor Lisa Klein Rutgers, the State University of New Jersey INTRODUCTION
More informationLinear Algebra Done Wrong. Sergei Treil. Department of Mathematics, Brown University
Linear Algebra Done Wrong Sergei Treil Department of Mathematics, Brown University Copyright c Sergei Treil, 2004, 2009 Preface The title of the book sounds a bit mysterious. Why should anyone read this
More informationOSCILLATION THEORY FOR DIFFERENCE AND FUNCTIONAL DIFFERENTIAL EQUATIONS
OSCILLATION THEORY FOR DIFFERENCE AND FUNCTIONAL DIFFERENTIAL EQUATIONS Oscillation Theory for Difference and Functional Differential Equations by Ravi P. Agarwal Department of Mathematics, National University
More information