Entropy production from chaoticity in YangMills field theory with use of the Husimi function
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Abstract
We investigate possible entropy production in YangMills (YM) field theory by using a quantum distribution function called the Husimi function fH(A, E, t) for the YM field, which is given by a coarse graining of the Wigner function and nonnegative. We calculate the HusimiWehrl entropy SHW(t)=TrfHlogfH defined as an integral over the phase space, for which two adaptations of the testparticle 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 chaotic behavior in the classical limit. We also make a simplification of the multidimensional phasespace integrals by making a product ansatz for the Husimi function, which is found to give a 1020% overestimate of the HusimiWehrl 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 KolmogorovSinai entropy, suggesting that the chaoticity of the classical YM field causes the entropy production in the quantum YM theory.
Journal

 Physical Review D

Physical Review D 94(9), 20161101
American Physical Society