Quantum Work Relations and Response Theory in $\mathcal{PT}$-Symmetric Quantum Systems

TL;DR

This paper extends the universal quantum work relation and response theory to $ ext{PT}$-symmetric quantum systems with unbroken symmetry, revealing their validity and limitations in different symmetry regimes.

Contribution

It demonstrates that quantum work relations and response theory can be generalized to $ ext{PT}$-symmetric systems, highlighting the role of symmetry breaking.

Findings

Universal quantum work relation extends to unbroken $ ext{PT}$-symmetric systems.

Quantum Jarzynski equality and Onsager relations are recovered in this framework.

Relation fails in broken $ ext{PT}$-symmetry due to non-preservation of norm.

Abstract

In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extend to $\mathcal{PT}$-symmetric quantum system with unbroken $\mathcal{PT}$ symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory and Onsager reciprocal relations for the $\mathcal{PT}$-symmetric quantum system are recovered as special cases of the universal quantum work relation in $\mathcal{PT}$-symmetric quantum system. In the regime of broken $\mathcal{PT}$ symmetry, the universal quantum work relation does not hold as the norm is not preserved during the dynamics.