Entropy production in 2D $\lambda \phi^4$ theory in the Kadanoff-Baym approach

TL;DR

This paper investigates the non-equilibrium quantum dynamics and entropy production in a 1+1 dimensional scalar field theory using the Kadanoff-Baym approach, deriving a relativistic kinetic entropy that satisfies the H theorem.

Contribution

It extends the Kadanoff-Baym formalism to include NLO diagrams and derives a relativistic kinetic entropy, providing insights into thermalization in quantum field theory.

Findings

Kinetic entropy increases over time, approaching equilibrium.

The derived entropy satisfies the H theorem.

Numerical simulations show thermalization tendencies.

Abstract

We study non-equilibrium quantum dynamics of the single-component scalar field theory in 1+1 space-time dimensions on the basis of the Kadanoff-Baym equation including the next-to-leading-order (NLO) skeleton diagrams. As an extension of the non-relativistic case, we derive relativistic kinetic entropy at the first order in the gradient expansion of the Kadanoff-Baym equations. The derived entropy satisfies the H theorem. Next we perform numerical simulations in spatially homogeneous configurations to investigate thermalization properties of the system by evaluating the system entropy. We find that at later times the kinetic entropy increases approaching the equilibrium value, although the limited time interval in the early stage invalidates the use of it.