  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.
