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This paper investigates the thermodynamic properties of open $\mathcal{PT}$-symmetric quantum systems, specifically deriving ergotropy and verifying consistency with the laws of thermodynamics under non-Hermitian conditions. The work advances fundamental theoretical understanding in quantum mechanics by establishing a Hermitian basis for bi-orthonormal eigenvectors within this specific symmetry class. While relevant to foundational physics, it does not address current AI applications or practical quantum computing implementations.
Thermodynamics of an Open Two-Level $\mathcal{PT-}$Symmetric Quantum System
arXiv:2512.03935v2 Announce Type: replace Abstract: For a subclass of a general $\mathcal{PT}-$symmetric Hamiltonian obeying anti-commutation relation with its conjugate, a Hermitian basis is found that spans the bi-orthonormal energy eigenvectors. Using the modified projectors constructed from these eigenvectors, the generalized density matrix of the $\mathcal{PT}-$symmetric evolution is calculated, and subsequently, ergotropy for a closed system is obtained. The $\mathcal{PT}-$symmetric system, in an open system scenario, is studied to understand ergotropy under different regimes of non-Hermiticity of the Hamiltonian. The consistency of the three laws of thermodynamics for the $\mathcal{PT}-$symmetric system in an open system scenario is also analyzed.
Abstract:For a subclass of a general $\mathcal{PT}-$symmetric Hamiltonian obeying anti-commutation relation with its conjugate, a Hermitian basis is found that spans the bi-orthonormal energy eigenvectors. Using the modified projectors constructed from these eigenvectors, the generalized density matrix of the $\mathcal{PT}-$symmetric evolution is calculated, and subsequently, ergotropy for a closed system is obtained. The $\mathcal{PT}-$symmetric system, in an open system scenario, is studied to understand ergotropy under different regimes of non-Hermiticity of the Hamiltonian. The consistency of the three laws of thermodynamics for the $\mathcal{PT}-$symmetric system in an open system scenario is also analyzed.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2512.03935 [quant-ph]
(or arXiv:2512.03935v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2512.03935 Focus to learn more arXiv-issued DOI via DataCite
J. Phys. A: Math. Theor. 59, 345302 (2026)
https://doi.org/10.1088/1751-8121/ae98c7 Focus to learn more DOI(s) linking to related resources
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Full text under the publisher's open licence · 206 words
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