Thermodynamics of Quantum Heat Bath

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.

26 pages; version to appear in J. Phys. A

References in corpus (9)

• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• On the time scales in the approach to equilibrium of macroscopic quantum systems
• Thermal equilibration between two quantum systems
• Concentration of measure for quantum states with a fixed expectation value
• Solvable model of quantum microcanonical states
• Quantum Fluctuation Relations for Ensembles of Wave Functions
• A generalized quantum microcanonical ensemble
• Beyond quantum microcanonical statistics

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