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We investigate possible entropy production in Yang-Mills (YM) field theory byusing 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 andnon-negative. We calculate the Husimi-Wehrl (HW) entropy $S_{\rm HW}(t)=-{\rmTr}f_H \log f_H$ defined as an integral over the phase-space, for which twoadaptations of the test-particle method are used combined with Monte-Carlomethod. We utilize the semiclassical approximation to obtain the time evolutionof the distribution functions of the YM field, which is known to show a chaoticbehavior in the classical limit. We also make a simplification of themulti-dimensional phase-space integrals by making a product ansatz for theHusimi function, which is found to give a 10-20 per cent over estimate of theHW entropy for a quantum system with a few degrees of freedom. We show that thequantum YM theory does exhibit the entropy production, and that the entropyproduction rate agrees with the sum of positive Lyapunov exponents or theKolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YMfield causes the entropy production in the quantum YM theory.

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