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We study non-equilibrium quantum dynamics of the single-component scalarfield theory in 1+1 space-time dimensions on the basis of the Kadanoff-Baymequation including the next-to-leading-order (NLO) skeleton diagrams. As anextension of the non-relativistic case, we derive relativistic kinetic entropyat the first order in the gradient expansion of the Kadanoff-Baym equations.The derived entropy satisfies the H theorem. Next we perform numericalsimulations in spatially homogeneous configurations to investigatethermalization properties of the system by evaluating the system entropy. Wefind that at later times the kinetic entropy increases approaching theequilibrium value, although the limited time interval in the early stageinvalidates the use of it.

Entropy production in 2D $\lambda \phi^4$ theory in the Kadanoff-Baym approach