Generalization of thermodynamic potentials including information

In this work we analyze the connection between information theory and thermodynamics. Three different potentials are presented, all related to the Kullback–Leibler divergence. These potentials represent three different conditions of energy and information exchange between a reservoir and a subsystem. The first potential describes a situation where the two systems are exchanging energy without any external control. The second potential considers the situation where the reservoir can get information through the state of another secondary system about the internal state of the subsystem. This information can then be used by a Maxwell demon to increase the free energy of the subsystem. In this second scenario it is assumed that the energy cost of the information probe and the Maxwell demon are at the expense of the reservoir. Finally, a third case is considered where the information obtained through the secondary system is used not only to manipulate an internal Maxwell demon, but to perform directly work over the subsystem. This last case involves a direct modification of the Hamiltonian of the subsystem.