Free energy potential and temperature with information exchange

TL;DR

This paper introduces a generalized thermodynamic formalism incorporating information exchange, leading to a modified entropy and temperature concept that applies to both equilibrium and non-equilibrium steady states, demonstrated through a simple particle model.

Contribution

It develops a unified framework for thermodynamics with information exchange, extending temperature and entropy concepts to non-equilibrium steady states with a simple model example.

Findings

Extended formalism includes non-equilibrium steady states.

Non-equilibrium states can be mapped to equilibrium with generalized temperature.

Information exchange modifies entropy and temperature relations.

Abstract

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.