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Title: Bayesian second law of thermodynamics

Abstract

Here, we derive a generalization of the second law of thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically evolving system degrades over time. The Bayesian second law can be written as Δ H ( ρ m , ρ ) + 〈 Q 〉 F | m ≥ 0 , where Δ H ( ρ m , ρ ) is the change in the cross entropy between the original phase-space probability distribution ρ and the measurement-updated distribution ρ m and 〈 Q 〉 F | m is the expectation value of a generalized heat flow out of the system. Furthermore, we derive refined versions of the second law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of integral fluctuation theorems. We demonstrate the formalism using simple analytical and numerical examples.

Authors:
 [1];  [1];  [2];  [1]
+ Show Author Affiliations
  1. California Institute of Technology (CalTech), Pasadena, CA (United States)
  2. Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States); University of California, Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Gordon and Betty Moore Foundation
OSTI Identifier:
1600522
Alternate Identifier(s):
OSTI ID: 1280191
Grant/Contract Number:  
SC0011632; AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 94; Journal Issue: 2; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Bartolotta, Anthony, Carroll, Sean M., Leichenauer, Stefan, and Pollack, Jason. Bayesian second law of thermodynamics. United States: N. p., 2016. Web. doi:10.1103/PhysRevE.94.022102.
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Bartolotta, Anthony, Carroll, Sean M., Leichenauer, Stefan, & Pollack, Jason. Bayesian second law of thermodynamics. United States. https://doi.org/10.1103/PhysRevE.94.022102
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Bartolotta, Anthony, Carroll, Sean M., Leichenauer, Stefan, and Pollack, Jason. Mon . "Bayesian second law of thermodynamics". United States. https://doi.org/10.1103/PhysRevE.94.022102. https://www.osti.gov/servlets/purl/1600522.
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@article{osti_1600522,
title = {Bayesian second law of thermodynamics},
author = {Bartolotta, Anthony and Carroll, Sean M. and Leichenauer, Stefan and Pollack, Jason},
abstractNote = {Here, we derive a generalization of the second law of thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically evolving system degrades over time. The Bayesian second law can be written as ΔH(ρm,ρ)+〈Q〉F|m≥0, where ΔH(ρm,ρ) is the change in the cross entropy between the original phase-space probability distribution ρ and the measurement-updated distribution ρm and 〈Q〉F|m is the expectation value of a generalized heat flow out of the system. Furthermore, we derive refined versions of the second law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of integral fluctuation theorems. We demonstrate the formalism using simple analytical and numerical examples.},
doi = {10.1103/PhysRevE.94.022102},
journal = {Physical Review E},
number = 2,
volume = 94,
place = {United States},
year = {Mon Aug 01 00:00:00 EDT 2016},
month = {Mon Aug 01 00:00:00 EDT 2016}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/PhysRevE.94.022102
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