The basis of the Second Law of thermodynamics in quantum field theory

The result that closed systems evolve toward equilibrium is derived entirely on the basis of quantum field theory for a model system, without invoking any of the common extra-mathematical notions of particle trajectories, collapse of the wave function, measurement, or intrinsically stochastic processes. The equivalent of the Stosszahlansatz of classical statistical mechanics is found, and has important differences from the classical version. A novel result of the calculation is that interacting many-body systems in the infinite volume limit evolve toward diagonal states (states with loss of all phase information) on the time scale of the interaction time. The connection with the onset of off-diagonal phase coherence in Bose condensates is discussed.

► The quantum Boltzmann equation is derived rigorously for a closed many-particle system.
► The crucial role of dephasing in the irreversibility of the Second Law is shown.
► We show how this dephasing arises in a closed many-body system.
► Bose condensates (and all degenerate Bose systems) can spontaneously reverse this dephasing.
► In the infinite volume-limit, the Second Law is seen to be a deterministic law, not probabilistic.