Fluctuation theorems. Proseminar in theoretical physics Vincent Beaud ETH Zürich May 11th 2009
|
|
|
- Douglas Hoover
- 5 years ago
- Views:
Transcription
1 Fluctuation theorems Proseminar in theoretical physics Vincent Beaud ETH Zürich May 11th 2009
2 Outline Introduction Equilibrium systems Theoretical background Non-equilibrium systems Fluctuations and small systems: an example Fluctuation theorems Crooks fluctuation theorem Proof thereof Two particular cases: Jarzynski equality and Gallavotti- Cohen s fluctuation theorem Summary
3 Introduction: Equilibrium systems Equilibrium systems A thermodynamic system is said to be in thermodynamic equilibrium if where denotes the phase-space distribution at position and time. A thermodynamic system is in thermodynamic quasiequilibrium if varies very slowly in time. Equilibrium systems obey classical thermodynamics.
4 Introduction: Equilibrium systems Theoretical background 1 st law of thermodynamics: where is the heat transferred to the system. is the work performed upon it. 2 nd law of thermodynamics: or: The entropy of a thermally isolated system that is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
5 Introduction: Equilibrium systems Theoretical background (2) Consider a system coupled to a heat bath at constant temperature. If we perform some work upon the system, the total entropy change of the universe between its initial and final configurations is where is the free energy difference of the system. is the temperature of the heat bath.
6 Introduction: Non-equilibrium systems Non-equilibrium systems A thermodynamic system is said to be in thermodynamic non-equilibrium if where denotes the phase-space distribution at position and time. Systems that share energy with other systems are not in equilibrium. Most systems found in nature are not in equilibrium. Classical thermodynamics does not apply to these systems.
7 Introduction: Non-equilibrium systems Fluctuations and small systems Consider an ideal gas containing particles. The kinetic energy distribution of the particles is described by the Maxwell-Boltzmann distribution. Then and The fluctuations are of order.
8 Fluctuation theorems Fluctuation theorems Only a small number of variables are needed to describe an equilibrium system. Non-equilibrium systems cannot be described in that way. The control parameter is the variable that must be specified to unambiguously define the system s state, while other variables are allowed to fluctuate. e.g. string of monomers in water at constant temperature Control parameter: length Control parameter: force
9 Fluctuation theorems: Crooks' fluctuation theorem Crooks fluctuation theorem (CFT) G. E. Crooks, Phys. Rev. E 60, 2721 (1999) Consider some finite classical system coupled to a constant temperature heat bath. It is then driven out of equilibrium by some time-dependent work process described by a control parameter. The dynamics of the system are required to be: stochastic Markovian microscopically reversible
10 Fluctuation theorems: Crooks' fluctuation theorem Crooks fluctuation theorem (2) Then Crooks fluctuation theorem asserts where is the entropy production of the system and the heat bath over some time interval. the probability of a given entropy production along the forward / reverse path. CFT generalizes to systems coupled to a set of baths, each being characterized by a constant intensive parameter.
11 Fluctuation theorems: CFT consequences CFT: consequences Thus we have and we know that the entropy hence the entropy production is an extensive quantity, i.e. increases with increasing volume of the system. This statement solves Loschmidt s paradox: Since the microscopic laws of mechanics are invariant under time reversal, there must also exist entropydecreasing evolutions, in apparent violation of the 2 nd law.
12 Fluctuation theorems: Testing CFT Testing Crooks fluctuation theorem D. Collin et al., Nature 437, (2005) Difference in positions of the bottom and top beads as control parameter. Work needed to stretch the RNA molecule fluctuates.
13 Fluctuation theorems: Testing CFT Testing CFT (2) The unfolding and refolding processes need to be related by time-reversal symmetry. If the molecular transition starts in an equilibrium state and reach a well-defined final state. The CFT predicts: Since. The CFT does not require that the system studied reaches its final equilibrium state immediately after the unfolding and refolding processes have been completed.
14 Fluctuation theorems: Testing CFT
15 Fluctuation theorems: Proof of CFT Proof of CFT Consider a finite classical system coupled to a heat bath at constant temperature. State of the system specified by and. Particular path denoted by:, the corresponding reversed path by: where we shifted origin such that:
16 Fluctuation theorems: Proof of CFT Proof of CFT (2) Dynamics are stochastic, Markovian and satisfy the following microscopically reversible condition: where is the heat or amount of energy transferred to the system from the bath along the path. Let denote the phase-space distribution at time and position. To be continued on the white board.
17 Fluctuation theorems: CFT particular cases: Jarzynski's equality CFT: particular cases Jarzynski s equality C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997) It follows from CFT that for systems starting and ending in equilibrium Then integrating over yields Jarzynski s equality where the angle brackets denote an average over a large number of non-equilibrium processes between the two equilibrium states.
18 Fluctuation theorems: CFT particular cases: Jarzynski's equality Jarzynski s equality (2) Jarzynski s equality holds for systems driven arbitrarily far from equilibrium. Using Jensen s inequality for convex functions one can readily show that Jarzynski s equality implies the 2 nd law of thermodynamics Jarzynski s equality was successfully tested in 2002 by stretching a polymer between its folded and unfolded configuration, both reversibly and irreversibly.
19 Fluctuation theorems: CFT particular cases: Jarzynski's equality Testing Jarzynski s equality J. Liphardt et al., Science 296, 1832 (2002) Difference in positions of the bottom and top beads as control parameter. Work needed to stretch the RNA molecule fluctuates.
20 Fluctuation theorems: CFT particular cases: Jarzynski's equality Compare three different estimates for : the average work: the fluctuation dissipation estimate: the estimate from Jarzynski s equality:
21 Fluctuation theorems: CFT particular cases: Gallavotti-Cohen's fluctuation theorem CFT: particular cases (2) Gallavotti-Cohen s fluctuation theorem G. Gallavotti, E. Cohen, Phys. Rev. Lett. 74, 2694 (1995) A system driven by a time symmetric periodic process will settle into a non-equilibrium steady state. If we begin where the control parameter is also time symmetric, CFT is valid for any integer number of cycles and reads where is the entropy production of the system and the heat bath over some time interval. the probability of a given entropy production along the path.
22 Fluctuation theorems: CFT particular cases: Gallavotti-Cohen's fluctuation theorem GC fluctuation theorem (2) Since the system begins and ends in the same probability distribution, the average entropy production depends only on the average amount of heat transferred to the system. Approximation where is the heat transferred from the bath to the system during the time. In the long-time limit we obtain Gallavotti-Cohen s fluctuation theorem:
23 Fluctuation theorems: CFT particular cases: Gallavotti-Cohen's fluctuation theorem GC fluctuation theorem (2) Gallavotti-Cohen s fluctuation theorem simply ignores the relatively small and difficult to measure microscopic entropy of the system. It is only asymptotically true, whereas Crooks fluctuation theorem is valid at any time. It was successfully tested in 2005, collecting the probability distributions of power injected and dissipated by a small electrical dipole that was maintained in a non-equilibrium steady state by injection of a constant current. (N. Garnier and S. Ciliberto, Phys. Rev. Lett. 71, (2005))
24 Summary Summary Fluctuations cannot be neglected for small systems. There are only few analytic relations in the non-equilibrium thermodynamics of small systems: these are the so-called fluctuation theorems. Paths with negative entropy production are possible, but become exponentially unlikely for macroscopic systems (2 nd law of thermodynamics is not violated). Fluctuation theorems allow for a measurement of the free energy difference between two equilibrium states using non-equilibrium processes (CFT and Jarzynski equality).
The physics of information: from Maxwell s demon to Landauer. Eric Lutz University of Erlangen-Nürnberg
The physics of information: from Maxwell s demon to Landauer Eric Lutz University of Erlangen-Nürnberg Outline 1 Information and physics Information gain: Maxwell and Szilard Information erasure: Landauer
Fluctuations in Small Systems the case of single molecule experiments
Fluctuations in Small Systems the case of single molecule experiments Fabio Marchesoni, Università di Camerino, Italy Perugia, Aug. 2 nd, 2011 force distance k B T >> quantum scale I do not believe a word
Nonequilibrium thermodynamics at the microscale
Nonequilibrium thermodynamics at the microscale Christopher Jarzynski Department of Chemistry and Biochemistry and Institute for Physical Science and Technology ~1 m ~20 nm Work and free energy: a macroscopic
The Nonequilibrium Thermodynamics of Small Systems
The Nonequilibrium Thermodynamics of Small Systems The interactions of tiny objects with their environments are dominated by thermal fluctuations. Guided by theory and assisted by new micromanipulation
Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences
PHYSICAL REVIEW E VOLUME 60, NUMBER 3 SEPTEMBER 1999 Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences Gavin E. Crooks* Department of Chemistry, University
Fluctuation Theorems of Work and Entropy in Hamiltonian Systems
Fluctuation Theorems of Work and Entropy in Hamiltonian Systems Sourabh Lahiri and Arun M Jayannavar Fluctuation theorems are a group of exact relations that remain valid irrespective of how far the system
Emergent Fluctuation Theorem for Pure Quantum States
Emergent Fluctuation Theorem for Pure Quantum States Takahiro Sagawa Department of Applied Physics, The University of Tokyo 16 June 2016, YITP, Kyoto YKIS2016: Quantum Matter, Spacetime and Information
Irreversibility and the arrow of time in a quenched quantum system. Eric Lutz Department of Physics University of Erlangen-Nuremberg
Irreversibility and the arrow of time in a quenched quantum system Eric Lutz Department of Physics University of Erlangen-Nuremberg Outline 1 Physics far from equilibrium Entropy production Fluctuation
Thermodynamic Computing. Forward Through Backwards Time by RocketBoom
Thermodynamic Computing 1 14 Forward Through Backwards Time by RocketBoom The 2nd Law of Thermodynamics Clausius inequality (1865) S total 0 Total Entropy increases as time progresses Cycles of time R.Penrose
J. Stat. Mech. (2011) P07008
Journal of Statistical Mechanics: Theory and Experiment On thermodynamic and microscopic reversibility Gavin E Crooks Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA
Optimal Thermodynamic Control and the Riemannian Geometry of Ising magnets
Optimal Thermodynamic Control and the Riemannian Geometry of Ising magnets Gavin Crooks Lawrence Berkeley National Lab Funding: Citizens Like You! MURI threeplusone.com PRE 92, 060102(R) (2015) NSF, DOE
Statistical properties of entropy production derived from fluctuation theorems
Statistical properties of entropy production derived from fluctuation theorems Neri Merhav (1) and Yariv Kafri (2) (1) Department of Electrical Engineering, Technion, Haifa 32, Israel. (2) Department of
Entropy and irreversibility in gas dynamics. Joint work with T. Bodineau, I. Gallagher and S. Simonella
Entropy and irreversibility in gas dynamics Joint work with T. Bodineau, I. Gallagher and S. Simonella Kinetic description for a gas of hard spheres Hard sphere dynamics The system evolves under the combined
The Jarzynski Equation and the Fluctuation Theorem
The Jarzynski Equation and the Fluctuation Theorem Kirill Glavatskiy Trial lecture for PhD degree 24 September, NTNU, Trondheim The Jarzynski equation and the fluctuation theorem Fundamental concepts Statiscical
Flaw in Crooks fluctuation theorem
Flaw in Crooks fluctuation theorem Gokaran Shukla School of Physics, Trinity College, Dublin 2, Ireland (Dated: September 19, 2018) The existence of Crooks fluctuation theorem (even at microscopic level,
Non-Equilibrium Fluctuations in Expansion/Compression Processes of a Single-Particle Gas
Non-Equilibrium Fluctuations in Expansion/Compression Processes o a Single-Particle Gas Hyu Kyu Pa Department o Physics, UNIST IBS Center or Sot and Living Matter Page 1 November 8, 015, Busan Nonequilibrium
On the Asymptotic Convergence. of the Transient and Steady State Fluctuation Theorems. Gary Ayton and Denis J. Evans. Research School Of Chemistry
1 On the Asymptotic Convergence of the Transient and Steady State Fluctuation Theorems. Gary Ayton and Denis J. Evans Research School Of Chemistry Australian National University Canberra, ACT 0200 Australia
Fluctuation theorems: where do we go from here?
Fluctuation theorems: where do we go from here? D. Lacoste Laboratoire Physico-Chimie Théorique, UMR Gulliver, ESPCI, Paris Outline of the talk 1. Fluctuation theorems for systems out of equilibrium 2.
Entropy Production and Fluctuation Relations in NonMarkovian Systems
Entropy Production and Fluctuation Relations in NonMarkovian Systems Tapio Ala-Nissilä Department of Applied Physics and COMP CoE, Aalto University School of Science (formerly Helsinki University of Technology),
Introduction to Fluctuation Theorems
Hyunggyu Park Introduction to Fluctuation Theorems 1. Nonequilibrium processes 2. Brief History of Fluctuation theorems 3. Jarzynski equality & Crooks FT 4. Experiments 5. Probability theory viewpoint
Free energy recovery in single molecule experiments
Supplementary Material Free energy recovery in single molecule experiments Single molecule force measurements (experimental setup shown in Fig. S1) can be used to determine free-energy differences between
Fluctuation Theorem for a Small Engine and Magnetization Switching by Spin Torque
Fluctuation Theorem for a Small Engine and Magnetization Switching by Spin Torque Yasuhiro Utsumi Tomohiro Taniguchi Mie Univ. Spintronics Research Center, AIST YU, Tomohiro Taniguchi, PRL 114, 186601,
Aspects of nonautonomous molecular dynamics
Aspects of nonautonomous molecular dynamics IMA, University of Minnesota, Minneapolis January 28, 2007 Michel Cuendet Swiss Institute of Bioinformatics, Lausanne, Switzerland Introduction to the Jarzynski
Mathematical Structures of Statistical Mechanics: from equilibrium to nonequilibrium and beyond Hao Ge
Mathematical Structures of Statistical Mechanics: from equilibrium to nonequilibrium and beyond Hao Ge Beijing International Center for Mathematical Research and Biodynamic Optical Imaging Center Peking
Introduction to Stochastic Thermodynamics: Application to Thermo- and Photo-electricity in small devices
Université Libre de Bruxelles Center for Nonlinear Phenomena and Complex Systems Introduction to Stochastic Thermodynamics: Application to Thermo- and Photo-electricity in small devices Massimiliano Esposito
Dissipation and the Relaxation to Equilibrium
1 Dissipation and the Relaxation to Equilibrium Denis J. Evans, 1 Debra J. Searles 2 and Stephen R. Williams 1 1 Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia
arxiv: v2 [cond-mat.stat-mech] 16 Mar 2012
![arxiv: v2 [cond-mat.stat-mech] 16 Mar 2012](/thumbs/73/68169064.jpg "arxiv: v2 [cond-mat.stat-mech] 16 Mar 2012")
arxiv:119.658v2 cond-mat.stat-mech] 16 Mar 212 Fluctuation theorems in presence of information gain and feedback Sourabh Lahiri 1, Shubhashis Rana 2 and A. M. Jayannavar 3 Institute of Physics, Bhubaneswar
Experimental demonstration that a strongly coupled plasma obeys the fluctuation theorem for entropy production
Experimental demonstration that a strongly coupled plasma obeys the fluctuation theorem for entropy production Chun-Shang Wong, J. Goree, Zach Haralson, and Bin Liu Department of Physics and Astronomy,
G : Statistical Mechanics Notes for Lecture 3 I. MICROCANONICAL ENSEMBLE: CONDITIONS FOR THERMAL EQUILIBRIUM Consider bringing two systems into
G25.2651: Statistical Mechanics Notes for Lecture 3 I. MICROCANONICAL ENSEMBLE: CONDITIONS FOR THERMAL EQUILIBRIUM Consider bringing two systems into thermal contact. By thermal contact, we mean that the
Entropy production and time asymmetry in nonequilibrium fluctuations
Entropy production and time asymmetry in nonequilibrium fluctuations D. Andrieux and P. Gaspard Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus
arxiv:cond-mat/ v2 [cond-mat.stat-mech] 25 Sep 2000
![arxiv:cond-mat/ v2 [cond-mat.stat-mech] 25 Sep 2000](/thumbs/92/109029912.jpg "arxiv:cond-mat/ v2 [cond-mat.stat-mech] 25 Sep 2000")
technical note, cond-mat/0009244 arxiv:cond-mat/0009244v2 [cond-mat.stat-mech] 25 Sep 2000 Jarzynski Relations for Quantum Systems and Some Applications Hal Tasaki 1 1 Introduction In a series of papers
arxiv: v2 [cond-mat.stat-mech] 18 Jun 2009
![arxiv: v2 [cond-mat.stat-mech] 18 Jun 2009](/thumbs/95/123892011.jpg "arxiv: v2 [cond-mat.stat-mech] 18 Jun 2009")
Memory erasure in small systems Raoul Dillenschneider and Eric Lutz Department of Physics, University of Augsburg, D-86135 Augsburg, Germany arxiv:811.351v2 [cond-mat.stat-mech] 18 Jun 29 We consider an
Thermodynamics for small devices: From fluctuation relations to stochastic efficiencies. Massimiliano Esposito
Thermodynamics for small devices: From fluctuation relations to stochastic efficiencies Massimiliano Esposito Beijing, August 15, 2016 Introduction Thermodynamics in the 19th century: Thermodynamics in
Stochastic thermodynamics
University of Ljubljana Faculty of Mathematics and Physics Seminar 1b Stochastic thermodynamics Author: Luka Pusovnik Supervisor: prof. dr. Primož Ziherl Abstract The formulation of thermodynamics at a
Beyond the Second Law of Thermodynamics
Beyond the Second Law of Thermodynamics C. Van den Broeck R. Kawai J. M. R. Parrondo Colloquium at University of Alabama, September 9, 2007 The Second Law of Thermodynamics There exists no thermodynamic
Fluctuation theorem in systems in contact with different heath baths: theory and experiments.
Fluctuation theorem in systems in contact with different heath baths: theory and experiments. Alberto Imparato Institut for Fysik og Astronomi Aarhus Universitet Denmark Workshop Advances in Nonequilibrium
The 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
Contents. 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
LANGEVIN EQUATION AND THERMODYNAMICS
LANGEVIN EQUATION AND THERMODYNAMICS RELATING STOCHASTIC DYNAMICS WITH THERMODYNAMIC LAWS November 10, 2017 1 / 20 MOTIVATION There are at least three levels of description of classical dynamics: thermodynamic,
Non-equilibrium phenomena and fluctuation relations
Non-equilibrium phenomena and fluctuation relations Lamberto Rondoni Politecnico di Torino Beijing 16 March 2012 http://www.rarenoise.lnl.infn.it/ Outline 1 Background: Local Thermodyamic Equilibrium 2
84 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
Fluctuation theorem between non-equilibrium states in an RC circuit
arxiv:1502.00571v3 [cond-mat.stat-mech] 20 Apr 2015 Fluctuation theorem between non-equilibrium states in an RC circuit Léo Granger 1,5, Jumna Mehlis 2,3, Édgar Roldán3,5, Sergio Ciliberto 4, and Holger
Fluctuation Relations for Stochastic Systems far from Equilibrium
Fluctuation Relations for Stochastic Systems far from Equilibrium Sven Dorosz Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of
Lecture 6: Irreversible Processes
Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP4, Thermodynamics and Phase Diagrams, H. K. D. H. Bhadeshia Lecture 6: Irreversible Processes Thermodynamics generally
Instantaneous gelation in Smoluchowski s coagulation equation revisited
Instantaneous gelation in Smoluchowski s coagulation equation revisited Colm Connaughton Mathematics Institute and Centre for Complexity Science, University of Warwick, UK Collaborators: R. Ball (Warwick),
Deriving Thermodynamics from Linear Dissipativity Theory
Deriving Thermodynamics from Linear Dissipativity Theory Jean-Charles Delvenne Université catholique de Louvain Belgium Henrik Sandberg KTH Sweden IEEE CDC 2015, Osaka, Japan «Every mathematician knows
arxiv:cond-mat/ v2 [cond-mat.soft] 29 Nov 2004
![arxiv:cond-mat/ v2 [cond-mat.soft] 29 Nov 2004](/thumbs/80/82235863.jpg "arxiv:cond-mat/ v2 [cond-mat.soft] 29 Nov 2004")
arxiv:cond-mat/411654v2 [cond-mat.soft] 29 Nov 24 ork probability distribution in single molecule experiments Alberto Imparato ( ) and Luca Peliti ( ) Dipartimento di Scienze Fisiche and Unità INFM, Università
The Nonequilibrium Thermodynamics of Small Systems
The Nonequilibrium Thermodynamics of Small Systems The interactions of tiny objects with their environments are dominated by thermai fiuctuations. Guided by theory and assisted by new micromanlpuiation
Statistical 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
PAPER No. 6: PHYSICAL CHEMISTRY-II (Statistical
Subject Paper No and Title Module No and Title Module Tag 6: PHYSICAL CHEMISTRY-II (Statistical 1: Introduction to Statistical CHE_P6_M1 TABLE OF CONTENTS 1. Learning Outcomes 2. Statistical Mechanics
Proteins polymer molecules, folded in complex structures. Konstantin Popov Department of Biochemistry and Biophysics
Proteins polymer molecules, folded in complex structures Konstantin Popov Department of Biochemistry and Biophysics Outline General aspects of polymer theory Size and persistent length of ideal linear
Numerical study of the steady state fluctuation relations far from equilibrium
Numerical study of the steady state fluctuation relations far from equilibrium Stephen R. Williams, Debra J. Searles, and Denis J. Evans Citation: The Journal of Chemical Physics 124, 194102 (2006); doi:
Chapter 2. Dielectric Theories
Chapter Dielectric Theories . Dielectric Theories 1.1. Introduction Measurements of dielectric properties of materials is very important because it provide vital information regarding the material characteristics,
The propagation of chaos for a rarefied gas of hard spheres
The propagation of chaos for a rarefied gas of hard spheres Ryan Denlinger 1 1 University of Texas at Austin 35th Annual Western States Mathematical Physics Meeting Caltech February 13, 2017 Ryan Denlinger
arxiv: v2 [cond-mat.stat-mech] 28 Mar 2013
![arxiv: v2 [cond-mat.stat-mech] 28 Mar 2013](/thumbs/72/66486526.jpg "arxiv: v2 [cond-mat.stat-mech] 28 Mar 2013")
Distribution of Entropy Production in a Single-Electron Box arxiv:303.6405v2 [cond-mat.stat-mech] 28 Mar 203 J. V. Koski, T. Sagawa, 2 O.-P. Saira,,3 Y. Yoon, A. Kutvonen, 4 P. Solinas,,4 M. Möttönen,,5
REGULARIZATION AND BOUNDARY CONDITIONS FOR THE 13 MOMENT EQUATIONS
1 REGULARIZATION AND BOUNDARY CONDITIONS FOR THE 13 MOMENT EQUATIONS HENNING STRUCHTRUP ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland (on leave from University of Victoria,
This is an author produced version of Statistical mechanics far from equilibrium: Prediction and test for a sheared system.
This is an author produced version of Statistical mechanics far from equilibrium: Prediction and test for a sheared system. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/74857/
17-1 Ideal Gases. Gases are the easiest state of matter to describe - All ideal gases exhibit similar behavior.
17-1 Ideal Gases Gases are the easiest state of matter to describe - All ideal gases exhibit similar behavior. An ideal gas is one that is thin enough, that the interactions between molecules can be ignored.
Chapter 4: Going from microcanonical to canonical ensemble, from energy to temperature.
Chapter 4: Going from microcanonical to canonical ensemble, from energy to temperature. All calculations in statistical mechanics can be done in the microcanonical ensemble, where all copies of the system
From fully quantum thermodynamical identities to a second law equality
From fully quantum thermodynamical identities to a second law equality Alvaro Alhambra, Lluis Masanes, Jonathan Oppenheim, Chris Perry Fluctuating States Phys. Rev. X 6, 041016 (2016) Fluctuating Work
arxiv:physics/ v2 [physics.class-ph] 18 Dec 2006
![arxiv:physics/ v2 [physics.class-ph] 18 Dec 2006](/thumbs/74/69907237.jpg "arxiv:physics/ v2 [physics.class-ph] 18 Dec 2006")
Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer arxiv:physics/061167v [physicsclass-ph] 18 Dec 006 Kevin Wood 1 C Van den roeck 3 R Kawai 4 and Katja Lindenberg
Experimental Rectification of Entropy Production by Maxwell s Demon in a Quantum System
Experimental Rectification of Entropy Production by Maxwell s Demon in a Quantum System Tiago Barbin Batalhão SUTD, Singapore Work done while at UFABC, Santo André, Brazil Singapore, January 11th, 2017
to satisfy the large number approximations, W W sys can be small.
Chapter 12. The canonical ensemble To discuss systems at constant T, we need to embed them with a diathermal wall in a heat bath. Note that only the system and bath need to be large for W tot and W bath
Fundamental work cost of quantum processes
1607.03104 1709.00506 Fundamental work cost of quantum processes Philippe Faist 1,2, Renato Renner 1 1 Institute for Theoretical Physics, ETH Zurich 2 Institute for Quantum Information and Matter, Caltech
The Kawasaki Identity and the Fluctuation Theorem
Chapter 6 The Kawasaki Identity and the Fluctuation Theorem This chapter describes the Kawasaki function, exp( Ω t ), and shows that the Kawasaki function follows an identity when the Fluctuation Theorem
Nonequilibrium fluctuations in small systems: From physics to biology
Nonequilibrium fluctuations in small systems: From physics to biology F Ritort Department de Fisica Fonamental, Faculty of Physics, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain; E-Mail:
Nonequilibrium Steady State of a Nanometric Biochemical System: Determining the Thermodynamic Driving Force from Single Enzyme Turnover Time Traces
Nonequilibrium Steady State of a Nanometric Biochemical System: Determining the Thermodynamic Driving Force from Single Enzyme Turnover Time Traces NANO LETTERS 005 Vol. 5, No. 1 373-378 Wei Min, Liang
Physics 172H Modern Mechanics
Physics 172H Modern Mechanics Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TAs: Alex Kryzwda John Lorenz akryzwda@purdue.edu jdlorenz@purdue.edu Lecture 22: Matter & Interactions, Ch.
STATIONARY NON EQULIBRIUM STATES F STATES FROM A MICROSCOPIC AND A MACROSCOPIC POINT OF VIEW
STATIONARY NON EQULIBRIUM STATES FROM A MICROSCOPIC AND A MACROSCOPIC POINT OF VIEW University of L Aquila 1 July 2014 GGI Firenze References L. Bertini; A. De Sole; D. G. ; G. Jona-Lasinio; C. Landim
Symmetry of the Dielectric Tensor
Symmetry of the Dielectric Tensor Curtis R. Menyuk June 11, 2010 In this note, I derive the symmetry of the dielectric tensor in two ways. The derivations are taken from Landau and Lifshitz s Statistical
A Study of the Thermal Properties of a One. Dimensional Lennard-Jones System
A Study of the Thermal Properties of a One Dimensional Lennard-Jones System Abstract In this study, the behavior of a one dimensional (1D) Lennard-Jones (LJ) system is simulated. As part of this research,
Spring_#8. Thermodynamics. Youngsuk Nam
Spring_#8 Thermodynamics Youngsuk Nam ysnam1@khu.ac.krac kr Ch.7: Entropy Apply the second law of thermodynamics to processes. Define a new property called entropy to quantify the secondlaw effects. Establish
Efficiency at Maximum Power in Weak Dissipation Regimes
Efficiency at Maximum Power in Weak Dissipation Regimes R. Kawai University of Alabama at Birmingham M. Esposito (Brussels) C. Van den Broeck (Hasselt) Delmenhorst, Germany (October 10-13, 2010) Contents
The existence of Burnett coefficients in the periodic Lorentz gas
The existence of Burnett coefficients in the periodic Lorentz gas N. I. Chernov and C. P. Dettmann September 14, 2006 Abstract The linear super-burnett coefficient gives corrections to the diffusion equation
Onsager theory: overview
Onsager theory: overview Pearu Peterson December 18, 2006 1 Introduction Our aim is to study matter that consists of large number of molecules. A complete mechanical description of such a system is practically
Even if you're not burning books, destroying information generates heat.
Even if you're not burning books, destroying information generates heat. Information and Thermodynamics: Experimental verification of Landauer's erasure principle with a colloidal particle Antoine Bérut,
Thermodynamics, 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...
Entropy and Free Energy in Biology
Entropy and Free Energy in Biology Energy vs. length from Phillips, Quake. Physics Today. 59:38-43, 2006. kt = 0.6 kcal/mol = 2.5 kj/mol = 25 mev typical protein typical cell Thermal effects = deterministic
III. Kinetic Theory of Gases
III. Kinetic Theory of Gases III.A General Definitions Kinetic theory studies the macroscopic properties of large numbers of particles, starting from their (classical) equations of motion. Thermodynamics
Optimal quantum driving of a thermal machine
Optimal quantum driving of a thermal machine Andrea Mari Vasco Cavina Vittorio Giovannetti Alberto Carlini Workshop on Quantum Science and Quantum Technologies ICTP, Trieste, 12-09-2017 Outline 1. Slow
Optimum protocol for fast-switching free-energy calculations
PHYSICAL REVIEW E 8, 7 Optimum protocol for fast-switching free-energy calculations Philipp Geiger and Christoph Dellago* Faculty of Physics, University of Vienna, Boltzmanngasse 5, 9 Vienna, Austria Received
Contrasting measures of irreversibility in stochastic and deterministic dynamics
Contrasting measures of irreversibility in stochastic and deterministic dynamics Ian Ford Department of Physics and Astronomy and London Centre for Nanotechnology UCL I J Ford, New J. Phys 17 (2015) 075017
Time-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
Lecture 6 Gas Kinetic Theory and Boltzmann Equation
GIAN Course on Rarefied & Microscale Gases and Viscoelastic Fluids: a Unified Framework Lecture 6 Gas Kinetic Theory and Boltzmann Equation Feb. 23 rd ~ March 2 nd, 2017 R. S. Myong Gyeongsang National
Lecture 34 Protein Unfolding Thermodynamics
Physical Principles in Biology Biology 3550 Fall 2018 Lecture 34 Protein Unfolding Thermodynamics Wednesday, 21 November c David P. Goldenberg University of Utah goldenberg@biology.utah.edu Clicker Question
Curriculum Vitae of Sergio Ciliberto
Curriculum Vitae of Sergio Ciliberto Personal Born: 18 June 1953 Family status: Married, one son and two daughters Citizenship: Italian Email: sergio.ciliberto@ens-lyon.fr Phone: +33 4 72 72 81 43 Last
Multicanonical distribution and the origin of power laws. Abstract
Multicanonical distribution and the origin of power laws G. L. Vasconcelos and D. S. P. Salazar Departamento de Física, Universidade Federal de Pernambuco, Brazil. and arxiv:128.5624v1 [cond-mat.stat-mech]
Nonintegrability and the Fourier heat conduction law
Nonintegrability and the Fourier heat conduction law Giuliano Benenti Center for Nonlinear and Complex Systems, Univ. Insubria, Como, Italy INFN, Milano, Italy In collaboration with: Shunda Chen, Giulio
Second 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
Irreversibility and the Second Law in Thermodynamics and Statistical Mechanics
Irreversibility and the Second Law in Thermodynamics and Statistical Mechanics Erik Curiel Munich Center For Mathematical Philosophy Ludwig-Maximilians-Universität and Black Hole Initiative Harvard University
Entropic forces in Brownian motion
Entropic forces in Brownian motion Nico Roos* Leiden Observatory, PO Box 9513, NL-2300 RA Leiden, The Netherlands Interest in the concept of entropic forces has risen considerably since E. Verlinde proposed
Spin Superfluidity and Graphene in a Strong Magnetic Field
Spin Superfluidity and Graphene in a Strong Magnetic Field by B. I. Halperin Nano-QT 2016 Kyiv October 11, 2016 Based on work with So Takei (CUNY), Yaroslav Tserkovnyak (UCLA), and Amir Yacoby (Harvard)
Reversibility. Processes in nature are always irreversible: far from equilibrium
Reversibility Processes in nature are always irreversible: far from equilibrium Reversible process: idealized process infinitely close to thermodynamic equilibrium (quasi-equilibrium) Necessary conditions
Thermodynamics and Statistical Physics. Preliminary Ph.D. Qualifying Exam. Summer 2009
Thermodynamics and Statistical Physics Preliminary Ph.D. Qualifying Exam Summer 2009 (Choose 4 of the following 6 problems) -----------------------------------------------------------------------------------------------------------
Stochastic equations for thermodynamics
J. Chem. Soc., Faraday Trans. 93 (1997) 1751-1753 [arxiv 1503.09171] Stochastic equations for thermodynamics Roumen Tsekov Department of Physical Chemistry, University of Sofia, 1164 Sofia, ulgaria The
NON-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
A Deeper Look into Phase Space: The Liouville and Boltzmann Equations
A Deeper Look into Phase Space: The Liouville and Boltzmann Equations Brian Petko Statistical Thermodynamics Colorado School of Mines December 7, 2009 INTRODUCTION Phase Space, in a sense, can be a useful
Anatoly B. Kolomeisky. Department of Chemistry CAN WE UNDERSTAND THE COMPLEX DYNAMICS OF MOTOR PROTEINS USING SIMPLE STOCHASTIC MODELS?
Anatoly B. Kolomeisky Department of Chemistry CAN WE UNDERSTAND THE COMPLEX DYNAMICS OF MOTOR PROTEINS USING SIMPLE STOCHASTIC MODELS? Motor Proteins Enzymes that convert the chemical energy into mechanical
Lecture Outline Chapter 17. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 17 Physics, 4 th Edition James S. Walker Chapter 17 Phases and Phase Changes Ideal Gases Kinetic Theory Units of Chapter 17 Solids and Elastic Deformation Phase Equilibrium and
Nonequilibrium Thermodynamics of Small Systems: Classical and Quantum Aspects. Massimiliano Esposito
Nonequilibrium Thermodynamics of Small Systems: Classical and Quantum Aspects Massimiliano Esposito Paris May 9-11, 2017 Introduction Thermodynamics in the 19th century: Thermodynamics in the 21th century: