Kinetic and thermodynamic temperatures in quantum systems

TL;DR

This paper introduces a formalism combining Gibbs-Shannon entropy and information thermodynamics to define a thermodynamic temperature in non-equilibrium quantum systems with discrete spectra, extending classical concepts.

Contribution

It develops a generalized De-Brujin identity for discrete, non-symmetric distributions and applies it to quantum systems, providing new insights into non-equilibrium thermodynamics.

Findings

Formalism recovers known equilibrium results

Defines a new thermodynamic temperature concept

Demonstrates application to a non-equilibrium quantum oscillator

Abstract

In this work we present a formalism to describe non equilibrium conditions in systems with a discretized energy spectrum, such as quantum systems. We develop a formalism based on a combination of Gibbs-Shannon entropy and information thermodynamics that arrives to a generalization of the De-Brujin identity applicable to discrete and non-symmetric distributions. This allows to define the concept of a thermodynamic temperature with a different, albeit complementary meaning to the equilibrium kinetic temperature of a system. The theory is applied to Bosonic and Fermionic cases represented by an harmonic oscillator and a single energy state, respectively. We show that the formalism correctly recovers known results at equilibrium, then we demonstrate an application to a genuine non equilibrium state: a coherent quantum oscillator.