Quantum entropy of systems described by non-Hermitian Hamiltonians

Abstract

We study the quantum entropy of systems that are described by general\nnon-Hermitian Hamiltonians, including those which can model the effects of\nsinks or sources. We generalize the von Neumann entropy to the non- Hermitian\ncase and find that one needs both the normalized and non-normalized density\noperators in order to properly describe irreversible processes. It turns out\nthat such a generalization monitors the onset of disorder in quantum\ndissipative systems. We give arguments for why one can consider the generalized\nentropy as the informational entropy describing the flow of information between\nthe system and the bath. We illustrate the theory by explicitly studying few\nsimple models, including tunneling systems with two energy levels and\nnon-Hermitian detuning.\n