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We study non-equilibrium quantum dynamics of the single-component scalar field theory in 1+1 space-time dimensions on the basis of the Kadanoff-Baym equation including the next-to-leadingorder (NLO) skeleton diagrams. As an extension of the non-relativistic case, we derive relativistic kinetic entropy at the first order in the gradient expansion of the Kadanoff-Baym equations. The derived entropy satisfies the H theorem. Next we perform numerical simulations in spatially homogeneous configurations to investigate thermalization properties of the system by evaluating the system entropy. We find that at later times the kinetic entropy increases approaching the equilibrium value, although the limited time interval in the early stage invalidates the use of it.

We propose to apply the two-particle irreducible (2PI) formalism to the problem of thermalization in heavy-ion collisions in the Color Glass Condensate (CGC) picture. We consider the 2PI effective action to three loops and derive a set of coupled equations for the classical Yang-Mills field and the quantum fluctuations in the boost invariant coordinate system. The initial condition and the relation to previous works are also discussed.

We study nonequilibrium processes of Quantum Electrodynamics (QED) with relativistic charged Bose fields. The aim is to describe thermal equilibration, based on the Klein–Gordon equation for background coherent fields and the Kadanoff–Baym (KB) equation including the leading-order (LO) self-energy of the coupling expansion (the Hartree–Fock approximation). We introduce a gauge invariant relativistic kinetic entropy current at the first-order in the gradient expansion of the KB equation and we show the proof of the H-theorem in d + 1 dimensions (d = 1, 2, 3) in the presence of nonzero background coherent fields. Finally, we present numerical simulation in 1 + 1 dimensions and aim to investigate whether decoherence of the system occurs or not. We find that equilibrium states are realized with remaining background coherent charged Bose and photon fields by preparing distributions of incoherent charged particles asymmetrically in frequency mode as initial conditions in the KB equation even if LO self-energy is present.

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