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We consider the stationary state of a Markov process on a bipartite systemfrom the perspective of stochastic thermodynamics. One subsystem is used toextract work from a heat bath while being affected by the second subsystem. Weshow that the latter allows for a transparent and thermodynamically consistentinterpretation of a Maxwell's demon. Moreover, we obtain an integralfluctuation theorem involving the transfer entropy from one subsystem to theother. Comparing three different inequalities, we show that the entropydecrease of the first subsystem provides a tighter bound on the rate ofextracted work than both the rate of transfer entropy from this subsystem tothe demon and the heat dissipated through the dynamics of the demon. The lattertwo rates cannot be ordered by an inequality as shown with the illustrativeexample of a four state system.

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