  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.
