Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

TL;DR

This study demonstrates that entropy production in quantum Yang-Mills field theory can be attributed to the chaotic behavior of the classical limit, using Husimi functions and semiclassical approximations.

Contribution

It introduces a method to calculate entropy production in quantum YM fields via Husimi functions, linking chaos and entropy growth in a novel way.

Findings

Quantum YM theory exhibits entropy production.

Entropy production rate matches Lyapunov exponents.

Chaoticity in classical YM causes quantum entropy growth.

Abstract

We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called Husimi function $f_{\rm H}(A, E, t)$ for YM field, which is given by a coarse graining of Wigner function and non-negative. We calculate the Husimi-Wehrl (HW) entropy $S_{\rm HW}(t)=-{\rm Tr}f_H \log f_H$ defined as an integral over the phase-space, for which two adaptations of the test-particle method are used combined with Monte-Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show a chaotic behavior in the classical limit. We also make a simplification of the multi-dimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20 per cent over estimate of the HW entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production, and that the entropy production rate agrees with the sum of positive Lyapunov exponents or the Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM field causes the entropy production in the quantum YM theory.