Kadanoff-Baym Approach to Entropy Production in O(N) Theory with Next-to-Leading Order Self-Energy

Abstract

Abstract We investigate entropy production in the O(N) scalar theory using the Kadanoff-Baym equation. We show that one of the candidate expressions of the kinetic entropy satisfies the H-theorem in the first order of the gradient expansion with the next-to-leading-order self-energy of the 1/N expansion in the symmetric phase, and that entropy production occurs as the Green's function evolves with nonzero collision term contributions. Entropy production stops at local thermal equilibrium where the collision term contribution vanishes and the maximal entropy state is realized. We numerically examine these features of entropy production in thermalization processes in 1+1 dimensions for a couple of homogeneous cases, where the thermalization can proceed only with the off-shell effects. We find that the entropy production rate γ is larger for smaller N and is found to follow γ ∝ (1/N)ν where δ ≳ 2 at strong coupling measured in the unit of bare mass (m), ⋋= 40 m2.