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

Abstract

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

6 pages

References in corpus (7)

• Fluctuation theorems: Work is not an observable
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Experimental Free Energy Surface Reconstruction From Single-Molecule Force Spectroscopy Using Jarzynski's Equality
• Observation of Lee-Yang zeros
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Quantum work relations and response theory
• Jarzynski equality in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics

Cited by in corpus (1)

• Work statistics in non-Hermitian evolutions with Hermitian endpoints