Abstract
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.
Highlights
Thermal fluctuations play an important role in the functioning of molecular machines: fluctuations mediate the exchange of energy between molecules and the environment, enabling molecules to overcome free energy barriers and to stabilize in low free energy regions
The Jarzynski equality, for example, links work to the change of equilibrium free energy [1], and the Crooks fluctuation theorem relates the probability of work to the dissipation of work [2] if we mention a few
Jinwoo and Tanaka [27,28] have shown that the Jarzynski equality and the Crooks fluctuation theorem hold even within an ensemble of trajectories conditioned on a fixed microstate at final time τ, where the local form of non-equilibrium free energy replaces the role of equilibrium free energy in the equations, making it clear that free energy of microstate xτ encodes the amount of supplied work for reaching xτ during processes λt
Summary
Thermal fluctuations play an important role in the functioning of molecular machines: fluctuations mediate the exchange of energy between molecules and the environment, enabling molecules to overcome free energy barriers and to stabilize in low free energy regions. Jinwoo and Tanaka [27,28] have shown that the Jarzynski equality and the Crooks fluctuation theorem hold even within an ensemble of trajectories conditioned on a fixed microstate at final time τ, where the local form of non-equilibrium free energy replaces the role of equilibrium free energy in the equations, making it clear that free energy of microstate xτ encodes the amount of supplied work for reaching xτ during processes λt. We show that mutual information of a correlated-microstates encodes the amount of entropy production within the ensemble of paths that reach the correlated-states This local version of the fluctuation theorem of information exchange provides much more detailed information for each correlated-microstates compared to the results in [25,26].
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