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

Understand

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.