Statistical Physics on the space (x,v) for dissipative systems and study of an ensemble of harmonic oscillators in a weak linear dissipative medium

TL;DR

This paper investigates the statistical properties of dissipative harmonic oscillators in phase space, deriving thermodynamic quantities in classical and quantum regimes, highlighting the influence of dissipation.

Contribution

It introduces a phase space approach to analyze dissipative systems and computes thermodynamic properties of harmonic oscillators considering weak dissipation, including quantum effects.

Findings

Classical entropy and free energy depend on dissipation.

Quantum thermodynamic quantities are influenced by dissipation.

Internal energy and specific heat are unaffected by dissipation in the classical case.

Abstract

We use the phase space position-velocity ($x,v$) to deal with the statistical properties of velocity dependent dynamical systems, like dissipative ones. Within this approach, we study the statistical properties of an ensemble of harmonic oscillators in a linear weak dissipative media. Using the Debye model of a crystal, we calculate at first order in the dissipative parameter the entropy, free energy, internal energy, equation of state and specific heat using the classical and quantum approaches. for the classical approach we found that the entropy, the equation of state, and the free energy depend on the dissipative parameter, but the internal energy and specific heat do not depend of it. For the quantum case, we found that all the thermodynamical quantities depend on this parameter.