The Basis of the Second Law of Thermodynamics in Quantum Field Theory

TL;DR

This paper derives the second law of thermodynamics within quantum field theory for a model system, showing systems evolve toward equilibrium without classical assumptions, and identifies a quantum analogue of classical statistical mechanics concepts.

Contribution

It provides a quantum field theory derivation of the second law, introducing a quantum version of the Stosszahlansatz and analyzing the evolution toward diagonal states in many-body systems.

Findings

Systems evolve toward diagonal states in the infinite volume limit.

The quantum Stosszahlansatz differs from the classical version.

Interaction timescales govern the loss of phase coherence.

Abstract

The result that closed systems evolve toward equilibrium is derived entirely on the basis of quantum field theory for a model system, without invoking any of the common extra-mathematical notions of particle trajectories, collapse of the wave function, measurement, or intrinsically stochastic processes. The equivalent of the Stosszahlansatz of classical statistical mechanics is found, and has important differences from the classical version. A novel result of the calculation is that interacting many-body systems in the infinite volume limit evolve toward diagonal states (states with loss of all phase information) on the the time scale of the interaction time. The connection with the onset of off-diagonal phase coherence in Bose condensates is discussed.