Three perspectives on entropy dynamics in a non-Hermitian two-state system
arXiv:2404.03492 · doi:10.1088/1402-4896/ad8e0c
Abstract
A comparative study of entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping. In this it is demonstrated that their differences are rooted in the treatment of the environmental coupling mode. For unbroken symmetry of the system, a notable characteristic feature of the perspective taken is the presence or absence of purity oscillations, with an associated entropy revival. The description of the system is then continued from its -symmetric pseudo-Hermitian phase into the regime of spontaneously broken symmetry, in the latter two approaches through a non-analytic operator-based continuation, yielding a Lindblad master equation based on the charge operator . This phase transition indicates a general connection between the pseudo-Hermitian closed-system and the Lindbladian open-system formalism through a spontaneous breakdown of the underlying physical reflection symmetry.
12 pages, 6 figures
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