Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a Maxwell’s demon interpretation

Abstract

We consider the stationary state of a Markov process on a bipartite system\nfrom the perspective of stochastic thermodynamics. One subsystem is used to\nextract work from a heat bath while being affected by the second subsystem. We\nshow that the latter allows for a transparent and thermodynamically consistent\ninterpretation of a Maxwell's demon. Moreover, we obtain an integral\nfluctuation theorem involving the transfer entropy from one subsystem to the\nother. Comparing three different inequalities, we show that the entropy\ndecrease of the first subsystem provides a tighter bound on the rate of\nextracted work than both the rate of transfer entropy from this subsystem to\nthe demon and the heat dissipated through the dynamics of the demon. The latter\ntwo rates cannot be ordered by an inequality as shown with the illustrative\nexample of a four state system.\n