Thermodynamics of Quantum Heat Bath

TL;DR

This paper develops a quantum heat bath model linking microscopic molecular properties to macroscopic thermodynamic behavior, highlighting how spectral features and probability measures influence the equation of state.

Contribution

It provides a general derivation of the quantum heat bath's equation of state considering molecular spectral properties and probability measures, advancing understanding of quantum thermodynamics.

Findings

The temperature-energy relation depends on molecular spectra and probability measures.

Microscopic features determine macroscopic thermodynamic properties.

Different hypotheses for equilibrium states can be compared using the model.

Abstract

A model for the thermodynamics of a quantum heat bath is introduced. Under the assumption that the bath molecules have finitely many degrees of freedom and are weakly interacting, we present a general derivation of the equation of state of the bath in the thermodynamic limit. The relation between the temperature and the specific energy of the bath depends on (i) the spectral properties of the molecules, and (ii) the choice of probability measure on the state space of a representative molecule. The results obtained illustrate how the microscopic features of the molecular constituents determine the macroscopic thermodynamic properties of the bath. Our findings can thus be used to compare the merits of different hypotheses for the equilibrium states of quantum systems. Two examples of plausible choices for the probability measure are considered in detail.