Thermodynamics of an Open $\mathcal{PT-}$Symmetric Quantum System

TL;DR

This paper explores the thermodynamics of a specific class of $ ext{PT}$-symmetric quantum systems, analyzing their energy, ergotropy, and thermodynamic laws in open system scenarios with non-Hermitian Hamiltonians.

Contribution

It introduces a Hermitian basis for a subclass of $ ext{PT}$-symmetric Hamiltonians and studies their thermodynamic properties, including ergotropy and thermodynamic law consistency, in open systems.

Findings

Derived a Hermitian basis for the energy eigenvectors.

Calculated the generalized density matrix and ergotropy.

Analyzed thermodynamic law consistency in open $ ext{PT}$-symmetric systems.

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.