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Free energy potential and temperature with information exchange

In this paper we develop a generalized formalism for equilibrium thermodynamic systems when an information is shared between the system and the reservoir. The information results in a correction to the entropy of the system. This extension of the formalism requires a consistent generalization of the concept of thermodynamic temperature. We show that this extended equilibrium formalism includes also non-equilibrium conditions in steady state. By non-equilibrium conditions we mean here a non Boltzmann probability distribution within the phase space of the system. It is in fact possible to map non-equilibrium steady state in an equivalent system in equilibrium conditions (Boltzmann distribution) with generalized temperature and the inclusion of the information potential corrections. A simple model consisting in a single free particle is discussed as elementary application of the theory.