Iida, H; Kunihiro, T; Müller, B; Ohnishi, A; Schäfer, A; Takahashi, TT, *Entropy production in classical Yang-Mills theory from glasma initial conditions*,
Physical Review D - Particles, Fields, Gravitation, and Cosmology, vol. 88 no. 9
(2013) [doi] .
**Abstract:**

*We study the thermalization process in classical Yang-Mills field theory starting from noisy glasmalike initial conditions by investigating the initial-value sensitivity of trajectories. Kunihiro et al. linked entropy generation to the Kolmogorov-Sinaï entropy, which gives the entropy production rate in classical chaotic systems, calculated numerically for classical Yang-Mills fields starting from purely random initial field configurations. In contrast, we study here glasmalike initial conditions. For small random fluctuations, we obtain qualitatively similar results, while no entropy increase is observed when such fluctuations are absent. We analyze the intermediate-time Lyapunov spectrum for several time windows and calculate the Kolmogorov-Sinaï entropy. We find a large number of positive Lyapunov exponents at the early stages of time evolution. Also, for later times, their number is a sizeable fraction of the total number of degrees of freedom. The spectrum of positive Lyapunov exponents at first changes rapidly but then stabilizes, indicating that the dynamics of the gauge fields approaches a steady state. Thus, we conclude that also for glasmalike initial conditions, a significant amount of entropy is produced by classical gluon field dynamics. © 2013 American Physical Society.*