Information and Physics Landauer Principle and Beyond
|
|
- Isaac Lynch
- 5 years ago
- Views:
Transcription
1 Information and Physics Landauer Principle and Beyond Ryoichi Kawai Department of Physics University of Alabama at Birmingham
2 Maxwell Demon Lerner, 975
3 Landauer principle Ralf Landauer ( ) Computational steps which inevitably require a minimal energy dissipation are those which discard information. (Landauer, 96) Any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information bearing degrees of freedom of the information processing apparatus or its environment. (Bennett, 982, Wikipedia) The erasure of one bit of information is necessarily accompanied by a dissipation of at least kt ln 2 heat. Key words: information, erasure, dissipation
4 Confusion If one were to imagine starting with those degrees of freedom in a thermalised state, there would be a real reduction in thermodynamic entropy if they were then re-set to a known state. This can only be achieved under information-preserving microscopically deterministic dynamics if the uncertainty is somehow dumped somewhere else i.e. if the entropy of the environment (or the non information-bearing degrees of freedom) is increased by at least an equivalent amount, as required by the Second Law, by gaining an appropriate quantity of heat: specifically kt ln 2 of heat for every bit of randomness erased. (Wikipedia, Information Theory and Physics) Landauer s principle for information erasure is valid for a symmetric doublewell potential, but not for an asymmetric one. The proof of W erase k T ln 2 using statistical mechanics is valid only for the symmetric case. (Sagawa and Ueda, 29)
5 Key word: Dissipation Which one is correct? W k T ln 2 Q k T ln 2 Δ S k ln 2 Δ S=k Δ H (H = information entropy) Δ S total k ln 2 Δ S total k I (erasure of one bit) (erasure of mutual information I)
6 Dissipation: Entropy production. Δ S total =Δ S sys +Δ S env Increase of total entropy in the universe. Information:? Erasure:?
7 What is information Erasure? Top Secret
8 Bit Eraser Which one erased the input information? Eraser Eraser How much energy dissipates?
9 Information is probabilistic transparent container H = H = H =ln 2 Information Entropy of one bit H = p ln p p ln p
10 Dissipation: Entropy production. Increase of total entropy in the universe. Information: Uncertainty of bits Ensemble of bits Erasure:?
11 Information Erasure E=mc 2 i ħ ψ t =H ψ t ρ=lρ reset to null randomize E=mc 2 i ħ ψ t =H ψ t ρ=lρ
12 Bit Eraser (Randomize) eraser eraser eraser / / / Δ H =ln 2 Δ H =ln 2 Δ H =
13 Bit Eraser (Reset to Zero) eraser eraser eraser Δ H = Δ H = Δ H = ln 2
14 Dissipation: Entropy production. Increase of total entropy in the universe. Information: Uncertainty of bits Ensemble of bits Erasure: For all possible input information, the outcome is the same. Any ensemble of bits is mapped to a standard ensemble. (There is a constraint to the mapping procedure.)
15 Implementation of Information in Physics: A model Z Microscopic state Z Ensemble Z p = Z p = p = 2 p = 2
16 A Physical Model: Randomizing Z Z Δ S total =?? Δ S total = Δ S total =k ln 2 Δ S total =k ln 2 Z Z?? Δ S total =k ln 2 Δ S total =
17 A Physical Model: Resetting to Zero y y W >, Q<?? Δ S total =k ln 2 x x Δ S total =k ln 2 y y W >, Q< W >, Q<?? x x Δ S total =k ln 2 Δ S total =
18 Dissipation: Entropy production. Increase of total entropy in the universe. Information: Uncertainty of bits Ensemble of bits Erasure: For all possible input information, the outcome is the same. Any ensemble of bits is mapped to a standard ensemble. The erasing procedure must be autonomous. (No feedback control.)
19 Bit Eraser (Randomize) eraser eraser eraser / / /// Δ I = Δ I = Δ I = ln 2
20 Bit Eraser (Reset to Zero) eraser eraser eraser Δ I = Δ I = Δ I = ln 2
21 Erasure of Mutual Information The bit eraser deleted the correlation between two bits of information. Input: (, R) and (, B) p R = 2, p B= 2, p R= p B = Output: (,R), (,B), (,R), and (,B) p R = p R = p B = p B = 4 Mutual Information between information and Y: I (,Y )=H ( )+H (Y ) H (,Y )=D( Y )= Y where I in =ln 2, I out = p = Y p Y, p Y = p Y p Y ln p Y p p Y When mutual information I(,Y) is erased, of entropy is generated. Δ S total k I (,Y )
22 More detailed analysis Δ S total =k D(ρ Γ (t) ρ Γ (t ))=k ρ Γ (q, p,t)ln ρ Γ(q, p,t) ρ Γ (q, p,t) (Kawai et al., 27) Information bearing coordinates: Other coordinates: Z Z? ρ(,t)= dz ρ Γ (q, p, t) Relation with information p i = d ρ(,t)χ i ( ), χ i ( )={ R i otherwise Δ S total D(ρ ρ) D ( p p), D( p p)= i p i ln p i p i
23 Landauer principle via free expansion Forward process: ρ( )={ Ω R R free expansion Backward process: ρ( )={ 2 Ω R 2 Ω R Z? Δ S total D(ρ ρ)=ln 2 Thermodynamics textbook says: Entropy increases during free expansion because information is lost. Landauer principle: When information is lost, entropy increases.
24 Proof of Δ S i I (,Y ) Y ρ(,y ) Hamiltonian: H (,Y ) H x ( )+H y (Y ) Forward: ρ (,Y ) ρ x ( )ρ y (Y ) ρ x ( )= dy ρ eq (, Y ), ρ y (Y )= d ρ eq (,Y ) Backward: ρ(,y )= ρ x ( ) ρ y (Y ) Y ρ(,y ) Δ S total =D(ρ ρ)= d dy ρ(,y )ln = d dy ρ(, Y )ln ρ(,y ) ρ(,y ) ρ(,y ) ρ x ( )ρ y (Y ) + d dy ρ(, Y )ln ρ ( )ρ (Y ) x y ρ x ( ) ρ y (Y ) =I (, Y )+D(ρ x ρ x )+ D(ρ y ρ y ) I (,Y )
25 The issue of asymmetric domain size Δ S total =k ln 3/2 2 3 V 3 V average: ln 3 ln 2>ln 2 2 Δ S total =k ln 3 W =kt ln 4 3, Δ S total=k ln 2 2 V 2 V W =kt ln 2 3, Δ S total=k ln 2 Sagawa and Ueda (29)
26 About Δ S=k Δ H When information entropy changes by H, the system entropy changes by S sys =k H. Since S total = S sys + S env >, S env >-k H. This information entropy is different from the one used to measure the uncertainty in information. Z Information flow diagram? Z? P = 2 P = 2 * Z? p = p 2 = 2 H = P ln P P ln P
27 Z? P = 2 Z? P = 2 Input has two possible perfectly certain states. H in =ln 2 Output is unique. H out = Δ H = ln 2 Δ S= k ln 2 Δ S env k ln 2 Entropy is transferred from information world to physical world. In this sense, the statement in Wikipedia is correct! This was Landauer's original idea but no physical basis has been offered.
28 Summary on Information Erasure Information is a profile of probability distribution: {p i } Relation between information and physics: p i = d ρ( )χ i ( ) Information erasure: {p i } {p i * } using an autonomous procedure (no feedback). p * (A single Hamiltonian for all initial conditions.) Remark: ρ(, t ) ρ * (, τ) is not necessary Amount of required entropy production depends on the initial condition (input information). 2 p The less uncertain is input, the larger is dissipation. If the input has no uncertainty, Δ S total k ln 2 If the input is completely uncertain, Δ S total p * Erasure of mutual information requires dissipation: Δ S total k I 2 p
29 Simple Logical Gates i i2 OR o Input: Two bits ; Output: One bit Erasure of one bit Δ S i k ln 2 dissipative Δ S i >? non-dissipative Δ S i Need work No work
30 Dissipation in an dissipative OR gate (information theory) Common argument in information theory using information flow P =P =P =P = 4 H =2ln 2 in P = 4, P = 3 4 H out =2 ln ln 3 Δ H = 3 4 ln 3 Δ S total = k Δ H =k 3 4 ln 3
31 Dissipation in an dissipative OR gate (physics) Assume that the input information has no uncertainty. Δ S total Δ S total k ln 3 Δ S i k ln 3 = k 3 4 ln 3
Comparative analysis of non-equilibrium quantum Landauer bounds
Comparative analysis of non-equilibrium quantum Landauer bounds Steve Campbell in collaboration with: Giacomo Guarnieri, Mauro Paternostro, and Bassano Vacchini To Appear July(ish) 2017 Landauer s Principle
More informationON BROWNIAN COMPUTATION
ON BROWNIAN COMPUTATION JOHN D. NORTON Department of History and Philosophy of Science Center for Philosophy of Science University of Pittsburgh Pittsburgh PA USA 15260 jdnorton@pitt.edu Draft: October10,
More informationBeyond 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
More informationThe (absence of a) relationship between thermodynamic and logical reversibility
The (absence of a) relationship between thermodynamic and logical reversibility arxiv:physics/0406137v1 [physics.hist-ph] 27 Jun 2004 O J E Maroney Imperial College London Physics Department The Blackett
More informationThermodynamic 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
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 informationThermodynamics of computation
C. THERMODYNAMICS OF COMPUTATION 37 C Thermodynamics of computation This lecture is based on Charles H. Bennett s The Thermodynamics of Computation a Review, Int. J. Theo. Phys., 1982 [B82]. Unattributed
More informationThe 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
More information2.2 Classical circuit model of computation
Chapter 2 Classical Circuit Models for Computation 2. Introduction A computation is ultimately performed by a physical device. Thus it is a natural question to ask what are the fundamental limitations
More information04. Information and Maxwell's Demon. I. Dilemma for Information-Theoretic Exorcisms.
04. Information and Maxwell's Demon. I. Dilemma for Information-Theoretic Exorcisms. Two Options: (S) (Sound). The combination of object system and demon forms a canonical thermal system. (P) (Profound).
More informationTransmitting and Hiding Quantum Information
2018/12/20 @ 4th KIAS WORKSHOP on Quantum Information and Thermodynamics Transmitting and Hiding Quantum Information Seung-Woo Lee Quantum Universe Center Korea Institute for Advanced Study (KIAS) Contents
More informationMaxwell s Demon. Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ (October 3, 2004)
1 Problem Maxwell s Demon Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (October 3, 2004) This problem is prob. 2 of [1]. One of the earliest conceptual supercomputers
More informationLandauer s principle in the quantum domain
Landauer s principle in the quantum domain Janet Anders Dept of Physics & Astronomy University College London London WC1E 6BT, UK j.anders@ucl.ac.uk Saroosh Shabbir Stefanie Hilt Department of Physics
More informationQuantum thermodynamics
Quantum thermodynamics a primer for the curious quantum mechanic Lídia del Rio, ETH Zurich QIP 2017 Seattle This talk is licensed under a Creative Commons Attribution 4.0 International License. Why quantum
More informationQuantum Thermodynamics
Quantum Thermodynamics In this chapter we wish to give some insights to quantum thermodynamics. It can be seen as an introduction to the topic, however not a broad one but rather an introduction by examples.
More informationMaxwell s Demon. Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ (October 3, 2004; updated September 20, 2016)
1 Problem Maxwell s Demon Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (October 3, 2004; updated September 20, 2016) This problem is prob. 2 of [1]. One of the
More informationEven 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,
More informationNotes on Landauer s principle, reversible computation, and Maxwell s Demon
Studies in History and Philosophy of Modern Physics 34 (2003) 501 510 Notes on Landauer s principle, reversible computation, and Maxwell s Demon Charles H. Bennett IBM Research Division, Yorktown Heights,
More informationQuantum computation: a tutorial
Quantum computation: a tutorial Samuel L. Braunstein Abstract: Imagine a computer whose memory is exponentially larger than its apparent physical size; a computer that can manipulate an exponential set
More informationThe End of the Thermodynamics of Computation: A No Go Result
December 22, 28, 2011 June 20, 2012 March 31, August 20, 2013 The End of the Thermodynamics of Computation: A No Go Result John D. Norton Department of History and Philosophy of Science Center for Philosophy
More informationConditioning, Correlation and Entropy Generation in Maxwell s Demon
Entropy 2013, 15, 4243-4265; doi:10.3390/e15104243 Article Conditioning, Correlation and Entropy Generation in Maxwell s Demon Neal G. Anderson OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy
More informationHardwiring Maxwell s Demon Tobias Brandes (Institut für Theoretische Physik, TU Berlin)
Hardwiring Maxwell s Demon Tobias Brandes (Institut für Theoretische Physik, TU Berlin) Introduction. Feedback loops in transport by hand. by hardwiring : thermoelectric device. Maxwell demon limit. Co-workers:
More informationNonequilibrium 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:
More informationDEMONS: MAXWELL S DEMON, SZILARD S ENGINE AND LANDAUER S ERASURE DISSIPATION
In: Proceedings of the first conference on Hot Topics in Physical Informatics (HoTPI, 2013 November). Paper is in press at International Journal of Modern Physics: Conference Series (2014). DEMONS: MAXWELL
More informationZero and negative energy dissipation at information-theoretic erasure
In press at J. Computational Electronics. http://vixra.org/abs/1507.0221 http://arxiv.org/abs/1507.08906 Zero and negative energy dissipation at information-theoretic erasure Laszlo Bela Kish, Claes-Göran
More informationPHYS 414 Problem Set 4: Demonic refrigerators and eternal sunshine
PHYS 414 Problem Set 4: Demonic refrigerators and eternal sunshine In a famous thought experiment discussing the second law of thermodynamics, James Clerk Maxwell imagined an intelligent being (a demon
More informationThermodynamics of feedback controlled systems. Francisco J. Cao
Thermodynamics of feedback controlled systems Francisco J. Cao Open-loop and closed-loop control Open-loop control: the controller actuates on the system independently of the system state. Controller Actuation
More informationThe first law of general quantum resource theories
The first law of general quantum resource theories Carlo Sparaciari 1, Lídia del Rio 2, Carlo Maria Scandolo 3, Philippe Faist 4, and Jonathan Oppenheim 1 1 Department of Physics and Astronomy, University
More informationInformation in Biology
Lecture 3: Information in Biology Tsvi Tlusty, tsvi@unist.ac.kr Living information is carried by molecular channels Living systems I. Self-replicating information processors Environment II. III. Evolve
More informationExperimental 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
More informationThermodynamic Cost Due to Changing the Initial Distribution Over States
Thermodynamic Cost Due to Changing the Initial Distribution Over States Artemy Kolchinsky David H. Wolpert SFI WORKING AER: 2016-07-014 SFI Working apers contain accounts of scienti5ic work of the author(s)
More informationInformation in Biology
Information in Biology CRI - Centre de Recherches Interdisciplinaires, Paris May 2012 Information processing is an essential part of Life. Thinking about it in quantitative terms may is useful. 1 Living
More informationLecture 27: Entropy and Information Prof. WAN, Xin
General Physics I Lecture 27: Entropy and Information Prof. WAN, Xin xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ 1st & 2nd Laws of Thermodynamics The 1st law specifies that we cannot get more energy
More informationInformation to energy conversion in an electronic Maxwell s demon and thermodynamics of measurements.
Information to energy conversion in an electronic Maxwell s demon and thermodynamics of measurements Stony Brook University, SUNY Dmitri V Averin and iang Deng Low-Temperature Lab, Aalto University Jukka
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 informationInformation Thermodynamics on Causal Networks
1/39 Information Thermodynamics on Causal Networks FSPIP 2013, July 12 2013. Sosuke Ito Dept. of Phys., the Univ. of Tokyo (In collaboration with T. Sagawa) ariv:1306.2756 The second law of thermodynamics
More information(# = %(& )(* +,(- Closed system, well-defined energy (or e.g. E± E/2): Microcanonical ensemble
Recall from before: Internal energy (or Entropy): &, *, - (# = %(& )(* +,(- Closed system, well-defined energy (or e.g. E± E/2): Microcanonical ensemble & = /01Ω maximized Ω: fundamental statistical quantity
More informationarxiv:quant-ph/ v1 4 Jul 2003
Measureament, Trace, Information Erasure and Entropy Qing-Yu Cai State Key of Laboratory of Magentic Resonance and Atom and Molecular Physics, Wuhan Institute of Physics and Mathematics, The Chinese Academy
More informationDemon Dynamics: Deterministic Chaos, the Szilard Map, & the Intelligence of Thermodynamic Systems.
Demon Dynamics: Deterministic Chaos, the Szilard Map, & the Intelligence of Thermodynamic Systems http://csc.ucdavis.edu/~cmg/ Jim Crutchfield Complexity Sciences Center Physics Department University of
More informationThermodynamics of Information Processing in Small Systems )
INVITED PAPERS 1 Progress of Theoretical Physics, Vol. 127, No. 1, January 2012 Thermodynamics of Information Processing in Small Systems ) Taahiro Sagawa 1,2 1 The Haubi Center, Kyoto University, Kyoto
More informationFrom 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
More informationarxiv:quant-ph/ v1 21 Feb 2002
QUANTUM DISCORD AND MAXWELL S DEMONS Wojciech Hubert Zurek Theory Division, T-6, MS B288, LANL, Los Alamos, NM87545 Abstract arxiv:quant-ph/0202123v1 21 Feb 2002 Quantum discord was proposed as an information
More informationMaxwell's Demons and Quantum Heat Engines in Superconducting Circuits
Maxwell's Demons and Quantum Heat Engines in Superconducting Circuits Jukka Pekola, Low Temperature Laboratory Aalto University, Helsinki, Finland Jonne Koski, now ETH Olli-Pentti Saira, now Caltech Ville
More informationQUANTUM INFORMATION -THE NO-HIDING THEOREM p.1/36
QUANTUM INFORMATION - THE NO-HIDING THEOREM Arun K Pati akpati@iopb.res.in Instititute of Physics, Bhubaneswar-751005, Orissa, INDIA and Th. P. D, BARC, Mumbai-400085, India QUANTUM INFORMATION -THE NO-HIDING
More informationarxiv: 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
More informationQuantum Thermodynamics
Quantum Thermodynamics Sai Vinjanampathy a and Janet Anders b a Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543. b Department of Physics and Astronomy,
More informationB. CONSERVATIVE LOGIC 19
B. CONSERVATIVE LOGIC 19 B Conservative logic These lectures are based primarily on Edward Fredkin and Tommaso To oli s Conservative logic, Int. J. Theo. Phys., 1982 [FT82]. B.1 Mechanical and thermal
More informationarxiv:chao-dyn/ v1 17 Feb 1999
Entropy Generation in Computation and the Second Law of Thermodynamics arxiv:chao-dyn/9902012v1 17 Feb 1999 Shunya Ishioka Department of Information Science, Kanagawa University Hiratsuka, Kanagawa 259-1293,
More informationExact Solutions of the Einstein Equations
Notes from phz 6607, Special and General Relativity University of Florida, Fall 2004, Detweiler Exact Solutions of the Einstein Equations These notes are not a substitute in any manner for class lectures.
More informationThermodynamic of computing. Fisica dell Energia - a.a. 2017/2018
Thermodynamic of computing Fisica dell Energia - a.a. 2017/2018 Landauer principle Minimum amount of energy required greater than zero Let assume the operation of bit reset # of initial states: 2 # of
More informationAn Introduction to Quantum Computation and Quantum Information
An to and Graduate Group in Applied Math University of California, Davis March 13, 009 A bit of history Benioff 198 : First paper published mentioning quantum computing Feynman 198 : Use a quantum computer
More informationQuantum heat engine using energy quantization in potential barrier
Quantum heat engine using energy quantization in potential barrier Sibasish Ghosh Optics and Quantum Information Group The Institute of Mathematical Sciences C.I.T. Campus, Taramani Chennai 600113. [In
More informationLecture 5: Temperature, Adiabatic Processes
Lecture 5: Temperature, Adiabatic Processes Chapter II. Thermodynamic Quantities A.G. Petukhov, PHYS 743 September 20, 2017 Chapter II. Thermodynamic Quantities Lecture 5: Temperature, Adiabatic Processes
More informationFundamental 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
More informationThermodynamic of computing. Fisica dell Energia - a.a. 2015/2016
Thermodynamic of computing Fisica dell Energia - a.a. 2015/2016 Landauer principle Minimum amount of energy required greater than zero Let assume the operation of bit reset # of initial states: 2 # of
More informationİlke Ercan, PhD Assistant Professor, Electrical & Electronics Eng. Dep. Boğaziçi University, İstanbul, Turkey
ENERGY EFFICIENCY LIMITS IN BROWNIAN CIRCUITS A PHYSICAL-INFORMATION-THEORETIC APPROACH, PhD Assistant Professor, Electrical & Electronics Eng. Dep. Boğaziçi University, İstanbul, Turkey Micro Energy 2017
More informationResponse to Comment on Zero and negative energy dissipation at information-theoretic erasure
Response to Comment on Zero and negative energy dissipation at information-theoretic erasure Laszlo Bela Kish, Claes-Göran Granqvist, Sunil P. Khatri, Ferdinand Peper Abstract We prove that statistical
More informationAveraging II: Adiabatic Invariance for Integrable Systems (argued via the Averaging Principle)
Averaging II: Adiabatic Invariance for Integrable Systems (argued via the Averaging Principle In classical mechanics an adiabatic invariant is defined as follows[1]. Consider the Hamiltonian system with
More informationAxiomatic Information Thermodynamics. Received: 1 February 2018; Accepted: 26 March 2018; Published: 29 March 2018
entropy Article Axiomatic Information Thermodynamics Austin Hulse 1, Benjamin Schumacher 1, * and Michael D. Westmoreland 2 1 Department of Physics, Kenyon College, Gambier, OH 43022, USA; hulsea@kenyon.edu
More informationPhysics, Time and Determinism
Physics, Time and Determinism M.P. Vaughan Free will and determinism Some definitions: 1. Free will is the capacity of an agent to chose a particular outcome 2. Determinism is the notion that all events
More informationRelating Maxwell s Demon and Quantitative Analysis of Information Leakage for Practical Imperative Programs
Relating Maxwell s Demon and Quantitative Analysis of Information Leakage for Practical Imperative Programs Kushal Anjaria, Arun Mishra To cite this version: Kushal Anjaria, Arun Mishra. Relating Maxwell
More informationMaxwell's Demon in Biochemical Signal Transduction
Maxwell's Demon in Biochemical Signal Transduction Takahiro Sagawa Department of Applied Physics, University of Tokyo New Frontiers in Non-equilibrium Physics 2015 28 July 2015, YITP, Kyoto Collaborators
More informationLandauer s Principle in Quantum Statistical Mechanics
Landauer s Principle in Quantum Statistical Mechanics Joint work with Vojkan Jakšić (McGill University) Claude-Alain Pillet (CPT Université de Toulon) Le Monde Quantique, IHES 18 mars 2015 Claude-Alain
More informationCHEM-UA 652: Thermodynamics and Kinetics
1 CHEM-UA 652: Thermodynamics and Kinetics Notes for Lecture 2 I. THE IDEAL GAS LAW In the last lecture, we discussed the Maxwell-Boltzmann velocity and speed distribution functions for an ideal gas. Remember
More informationarxiv: v4 [cond-mat.stat-mech] 3 Mar 2017
Memory Erasure using Time Multiplexed Potentials Saurav Talukdar, Shreyas Bhaban and Murti V. Salapaka University of Minnesota, Minneapolis, USA. (Dated: March, 7) arxiv:69.87v [cond-mat.stat-mech] Mar
More informationContrasting 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
More informationB.2 Mechanical and thermal modes
B. THERMODYNAMICS OF COMPUTATION 45 B.2 Mechanical and thermal modes This lecture is based primarily on Edward Fredkin and Tommaso To oli s Conservative logic (Fredkin & To oli, 1982). 1. We need to understand
More informationThermodynamical cost of accuracy and stability of information processing
Thermodynamical cost of accuracy and stability of information processing Robert Alicki Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdański, Poland e-mail: fizra@univ.gda.pl Fields Institute,
More informationPhysics of switches. Luca Gammaitoni NiPS Laboratory
Physics of switches Luca Gammaitoni NiPS Laboratory Logic switches A logic switch is a device that can assume physically distinct states as a result of external inputs. Usually the output of a physical
More informationarxiv:physics/ v2 [physics.class-ph] 9 Jan 2003
1 Notes on Landauer s Principle, Reversible Computation, and Maxwell s Demon arxiv:physics/0210005v2 [physics.class-ph] 9 Jan 2003 Charles H. Bennett IBM Research Division, Yorktown Heights, NY 10598,
More informationCompression and entanglement, entanglement transformations
PHYSICS 491: Symmetry and Quantum Information April 27, 2017 Compression and entanglement, entanglement transformations Lecture 8 Michael Walter, Stanford University These lecture notes are not proof-read
More informationInformation and thermodynamics: Experimental verification of Landauer s erasure principle
arxiv:153.6537v1 [cond-mat.stat-mech] 23 Mar 215 Information and thermodynamics: Experimental verification of Landauer s erasure principle Antoine Bérut, Artyom Petrosyan and Sergio Ciliberto Université
More informationThe 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
More informationEfficiency 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
More informationQuantum measurement theory
1 Quantum measurement theory 1.1 Introduction and overview Much that is studied in quantum measurement theory, and thus in this book, is very different from that studied in its classical counterpart, Bayesian
More informationLECTURE 4: Information-powered refrigerators; quantum engines and refrigerators
LECTURE 4: Information-powered refrigerators; quantum engines and refrigerators Fluctuation relations U. Seifert, Rep. Prog. Phys. 75, 126001 (2012) Fluctuation relations in a circuit Experiment on a double
More informationAxiomatic information thermodynamics
Axiomatic information thermodynamics arxiv:1801.05015v2 [quant-ph] 28 Mar 2018 Austin Hulse Benjamin Schumacher Department of Physics, Kenyon College Michael D. Westmoreland Department of Mathematics,
More informationStudies in History and Philosophy of Modern Physics
Studies in History and Philosophy of Modern Physics 42 (2011) 184 198 Contents lists available at ScienceDirect Studies in History and Philosophy of Modern Physics journal homepage: www.elsevier.com/locate/shpsb
More informationarxiv: 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
More informationarxiv: v2 [quant-ph] 3 May 2018
Verifying detailed fluctuation relations for discrete feedback-controlled quantum dynamics Patrice A. Camati 1, 1,, and Roberto M. Serra 1 Centro de Ciências Naturais e Humanas, Universidade ederal do
More informationInformation Equation of State
Entropy 2008, 10, 150-159; DOI: 10.3390/entropy-e10030150 Article Information Equation of State OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.org/entropy M. Paul Gough Space Science Centre, University of
More informationWhen Abandoned Bits Bite Back Reversibility and Quantum Computing
Area Exam February 4, 00 When Abandoned Bits Bite Back Reversibility and Quantum Computing Paul Fitzpatrick AI Lab, MIT, Cambridge, USA paulfitz@ai.mit.edu Abstract. Reversible logic was originally proposed
More informationTwo odd things about computation. Daniel Murfet University of Melbourne
Two odd things about computation Daniel Murfet University of Melbourne Two odd things I. Maxwell s demon (1871) Energy cost of computation II. Russell s paradox (1901) Time and space cost of computation
More informationHeat Machines (Chapters 18.6, 19)
eat Machines (hapters 8.6, 9) eat machines eat engines eat pumps The Second Law of thermodynamics Entropy Ideal heat engines arnot cycle Other cycles: Brayton, Otto, Diesel eat Machines Description The
More informationThe thermodynamics of cellular computation
The thermodynamics of cellular computation Sourjik and Wingreen (2012) Cur. Opinions in Cell Bio. Pankaj Mehta Collaborators: David Schwab, Charles Fisher, Mo Khalil Cells perform complex computations
More informationCentralized Versus Decentralized Control - A Solvable Stylized Model in Transportation Logistics
Centralized Versus Decentralized Control - A Solvable Stylized Model in Transportation Logistics O. Gallay, M.-O. Hongler, R. Colmorn, P. Cordes and M. Hülsmann Ecole Polytechnique Fédérale de Lausanne
More informationCentralized Versus Decentralized Control - A Solvable Stylized Model in Transportation
Centralized Versus Decentralized Control - A Solvable Stylized Model in Transportation M.-O. Hongler, O. Gallay, R. Colmorn, P. Cordes and M. Hülsmann Ecole Polytechnique Fédérale de Lausanne (EPFL), (CH)
More informationAY127 Problem Set 3, Winter 2018
California Institute of Technology AY27 Problem Set 3, Winter 28 Instructor: Sterl Phinney & Chuck Steidel TA: Guochao (Jason) Sun February 7, 28 Problem Detailed Solution : (a) We work in natural units
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 informationColloquium: The physics of Maxwell s demon and information
Colloquium: The physics of Maxwell s demon and information Koji Maruyama Advanced Science Institute, RIKEN (The Institute of Physical and Chemical Research), Wako-shi 351-0198, Japan and CREST, Japan Science
More informationTHE LANDAUER LIMIT AND THERMODYNAMICS OF BIOLOGICAL SYSTEMS
THE LANDAUER LIMIT AND THERMODYNAMICS OF BIOLOGICAL SYSTEMS Daid H. Wolpert Santa Fe Institute, MIT ttp://daidwolpert.weebly.com Jos Grocow Santa Fe Institute HEAT OF ERASING A BIT a) b) c) R 1 2 2R 1
More informationFrom the microscopic to the macroscopic world. Kolloqium April 10, 2014 Ludwig-Maximilians-Universität München. Jean BRICMONT
From the microscopic to the macroscopic world Kolloqium April 10, 2014 Ludwig-Maximilians-Universität München Jean BRICMONT Université Catholique de Louvain Can Irreversible macroscopic laws be deduced
More informationReversible computer hardware
Reversible computer hardware Alexis De Vos Imec v.z.w. and Universiteit Gent Belgium York, 22 March 2009 A logically irreversible computer 3 1 adding computer 4 3 1 adding computer 4?? adding computer
More informationThermodynamics: Entropy Conclusion
Thermodynamics: Entropy Conclusion From Warmup I would like to see an overview of all the chapters covered, and if possible some of the key concepts. I would appreciate a second opinion to make sure that
More informationPHYSICS OF QUANTUM COMPUTATION
XJ0300180 Письма в ЭЧАЯ. 2003. 1 [116] Particles and Nuclei, Letters. 2003. No. 1[116] PHYSICS OF QUANTUM COMPUTATION V. V. Belokurov, O. A. Khrustalev, V. A. Sadovnichy, O. D. Timofeevskaya Lomonosov
More informationAn Elementary Notion and Measurement of Entropy
(Source: Wikipedia: entropy; Information Entropy) An Elementary Notion and Measurement of Entropy Entropy is a macroscopic property of a system that is a measure of the microscopic disorder within the
More informationEstimating Accuracy in Classical Molecular Simulation
Estimating Accuracy in Classical Molecular Simulation University of Illinois Urbana-Champaign Department of Computer Science Institute for Mathematics and its Applications July 2007 Acknowledgements Ben
More informationWeeding Landauer s Garden
October 3, 2018 Weeding Landauer s Garden John D. Norton Department of History and Philosophy of Science University of Pittsburgh www.pitt.edu/~jdnorton Landauer s (1961) Irreversibility and Heat Generation
More informationFluctuation 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
More informationQuantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
Quantum and Information Thermodynamics: A nifying Framework based on Repeated Interactions Philipp trasberg, Gernot challer, and Tobias Brandes Institut für Theoretische Physik, Technische niversität Berlin,
More information