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Fluctuation Theorem of Information Exchange within an Ensemble of Paths Conditioned on Correlated-Microstates

Department of Mathematics, Kwangwoon University, 20 Kwangwoon-ro, Seoul 01897, Korea
Entropy 2019, 21(5), 477; https://doi.org/10.3390/e21050477
Received: 29 March 2019 / Revised: 2 May 2019 / Accepted: 6 May 2019 / Published: 7 May 2019
(This article belongs to the Special Issue Thermodynamics of Nonequilibrium Processes)
Fluctuation theorems are a class of equalities that express universal properties of the probability distribution of a fluctuating path functional such as heat, work or entropy production over an ensemble of trajectories during a non-equilibrium process with a well-defined initial distribution. Jinwoo and Tanaka (Jinwoo, L.; Tanaka, H. Sci. Rep. 2015, 5, 7832) have shown that work fluctuation theorems hold even within an ensemble of paths to each state, making it clear that entropy and free energy of each microstate encode heat and work, respectively, within the conditioned set. Here we show that information that is characterized by the point-wise mutual information for each correlated state between two subsystems in a heat bath encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange (Sagawa, T.; Ueda, M. Phys. Rev. Lett. 2012, 109, 180602) by showing that the fluctuation theorem holds even within an ensemble of paths that reach a correlated state during dynamic co-evolution of two subsystems. View Full-Text
Keywords: local non-equilibrium thermodynamics; fluctuation theorem; mutual information; entropy production; local mutual information; thermodynamics of information; stochastic thermodynamics local non-equilibrium thermodynamics; fluctuation theorem; mutual information; entropy production; local mutual information; thermodynamics of information; stochastic thermodynamics
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Jinwoo, L. Fluctuation Theorem of Information Exchange within an Ensemble of Paths Conditioned on Correlated-Microstates. Entropy 2019, 21, 477.

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