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A way to construct Boltzmann entropy, i.e., the entropy as a function of amicroscopic pure state, for quantum field systems is proposed. Operators thatshift the field in wavevector space are used in the construction. By employingan assumption, it is shown that, for almost all states in the ensemble of purestates corresponding to a thermodynamic state, the value of the proposedBoltzmann entropy coincides with that of the thermodynamic entropy for thethermodynamic state. For general self-interacting fields, the Boltzmann entropyevolves with time under Hamiltonian dynamics, so that it is capable ofcharacterizing the thermalization of isolated quantum field systems.

Boltzmann entropy for quantum field systems