For any diagonalisable non-Hermitian H with real spectrum, the biorthogonal Gibbs functional satisfies positivity of ω_bi(A†A) for all A if and only if H is quasi-Hermitian.
Non-hermitian quantum thermodynamics
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abstract
Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions. Namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Holographic dual of PT-symmetric BCFT via imaginary scalar on EOW brane shows spontaneous PT breaking and enhanced entanglement entropy growth in quenched state.
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Kubo-Martin-Schwinger conditions for non-Hermitian systems
For any diagonalisable non-Hermitian H with real spectrum, the biorthogonal Gibbs functional satisfies positivity of ω_bi(A†A) for all A if and only if H is quasi-Hermitian.
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Holographic Dual of PT Symmetric BCFT
Holographic dual of PT-symmetric BCFT via imaginary scalar on EOW brane shows spontaneous PT breaking and enhanced entanglement entropy growth in quenched state.