Boltzmann entropy for quantum field systems

TL;DR

This paper introduces a method to define Boltzmann entropy for quantum field systems using wavevector space operators, demonstrating its equivalence to thermodynamic entropy for most states and its evolution over time, capturing thermalization.

Contribution

It proposes a novel construction of Boltzmann entropy for quantum fields and shows its consistency with thermodynamic entropy and its dynamic evolution.

Findings

Boltzmann entropy matches thermodynamic entropy for most pure states.

The entropy evolves over time, indicating thermalization.

The method applies to self-interacting quantum fields.

Abstract

A way to construct Boltzmann entropy, i.e., the entropy as a function of a microscopic pure state, for quantum field systems is proposed. Operators that shift the field in wavevector space are used in the construction. By employing an assumption, it is shown that, for almost all states in the ensemble of pure states corresponding to a thermodynamic state, the value of the proposed Boltzmann entropy coincides with that of the thermodynamic entropy for the thermodynamic state. For general self-interacting fields, the Boltzmann entropy evolves with time under Hamiltonian dynamics, so that it is capable of characterizing the thermalization of isolated quantum field systems.