Maxwell's Demon walks into Wall Street: Stochastic thermodynamics meets expected utility theory

Andrés F. Ducuara; Paul Skrzypczyk; Francesco  Buscemi; Peter Sidajaya; Valerio Scarani

doi:10.1103/PhysRevLett.131.197103

Maxwell's Demon walks into Wall Street: Stochastic thermodynamics meets expected utility theory

Andrés F. Ducuara
, Paul Skrzypczyk
, Francesco Buscemi
, Peter Sidajaya
, Valerio Scarani

School of Physics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

13 Citations (Scopus)

71 Downloads (Pure)

Abstract

The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks’s fluctuation relations, every α Rényi divergence between the forward process and its reverse has the operational meaning of the “certainty equivalent” of dissipated work (or, more generally, of entropy production) for a player with risk aversion r=α−1. The two known cases α=1 and α=∞ are recovered and receive the new interpretation of being associated with a risk-neutral and an extreme risk-averse player, respectively. Among the new results, the condition for α=0 describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences

Original language	English
Article number	197103
Journal	Physical Review Letters
Volume	131
Issue number	19
Early online date	28 Oct 2023
DOIs	https://doi.org/10.1103/PhysRevLett.131.197103
Publication status	Published - 9 Nov 2023

Bibliographical note

Funding Information:
P. Sk. thanks Mate Arcos and Jonathan Oppenheim for interesting discussions, especially about their independent unpublished work connecting gambling and thermodynamics. A. F. D. acknowledges support from the International Research Unit of Quantum Information, Kyoto University, the Center for Gravitational Physics and Quantum Information (CGPQI), and from COLCIENCIAS 756-2016. P. Sk. acknowledges support from a Royal Society URF (NFQI) and is a CIFAR Azrieli Global Scholar in the Quantum Information Science Programme. F. B. acknowledges support from the MEXT-JSPS Grant-in-Aid for Transformative Research Areas (A) “Extreme Universe,” No. 21H05183; from the MEXT Quantum Leap Flagship Program (MEXT QLEAP) Grant No. JPMXS0120319794; from JSPS KAKENHI, Grants No. 20K03746 and No. 23K03230. P. Si. and V. S. are supported by the National Research Foundation, Singapore and A*STAR under its CQT Bridging Grant.

Publisher Copyright:
© 2023 American Physical Society.

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QITG
Bristol Quantum Information Institute

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10.1103/PhysRevLett.131.197103

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@article{723115a65e9743a6a5f69c3fca6d5cf8,

title = "Maxwell's Demon walks into Wall Street: Stochastic thermodynamics meets expected utility theory",

abstract = "The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks{\textquoteright}s fluctuation relations, every α R{\'e}nyi divergence between the forward process and its reverse has the operational meaning of the “certainty equivalent” of dissipated work (or, more generally, of entropy production) for a player with risk aversion r=α−1. The two known cases α=1 and α=∞ are recovered and receive the new interpretation of being associated with a risk-neutral and an extreme risk-averse player, respectively. Among the new results, the condition for α=0 describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences",

author = "Ducuara, \{Andr{\'e}s F.\} and Paul Skrzypczyk and Francesco Buscemi and Peter Sidajaya and Valerio Scarani",

note = "Funding Information: P. Sk. thanks Mate Arcos and Jonathan Oppenheim for interesting discussions, especially about their independent unpublished work connecting gambling and thermodynamics. A. F. D. acknowledges support from the International Research Unit of Quantum Information, Kyoto University, the Center for Gravitational Physics and Quantum Information (CGPQI), and from COLCIENCIAS 756-2016. P. Sk. acknowledges support from a Royal Society URF (NFQI) and is a CIFAR Azrieli Global Scholar in the Quantum Information Science Programme. F. B. acknowledges support from the MEXT-JSPS Grant-in-Aid for Transformative Research Areas (A) “Extreme Universe,” No. 21H05183; from the MEXT Quantum Leap Flagship Program (MEXT QLEAP) Grant No. JPMXS0120319794; from JSPS KAKENHI, Grants No. 20K03746 and No. 23K03230. P. Si. and V. S. are supported by the National Research Foundation, Singapore and A*STAR under its CQT Bridging Grant. Publisher Copyright: {\textcopyright} 2023 American Physical Society.",

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AU - Sidajaya, Peter

AU - Scarani, Valerio

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N2 - The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks’s fluctuation relations, every α Rényi divergence between the forward process and its reverse has the operational meaning of the “certainty equivalent” of dissipated work (or, more generally, of entropy production) for a player with risk aversion r=α−1. The two known cases α=1 and α=∞ are recovered and receive the new interpretation of being associated with a risk-neutral and an extreme risk-averse player, respectively. Among the new results, the condition for α=0 describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences

AB - The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks’s fluctuation relations, every α Rényi divergence between the forward process and its reverse has the operational meaning of the “certainty equivalent” of dissipated work (or, more generally, of entropy production) for a player with risk aversion r=α−1. The two known cases α=1 and α=∞ are recovered and receive the new interpretation of being associated with a risk-neutral and an extreme risk-averse player, respectively. Among the new results, the condition for α=0 describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences

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Maxwell's Demon walks into Wall Street: Stochastic thermodynamics meets expected utility theory

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Bibliographical note

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