Quantum work relations and response theory in parity-time-symmetric quantum systems

In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extends to a parity-time- ($\mathcal{PT}$-) 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 a $\mathcal{PT}$-symmetric quantum system. In the regime of broken $\mathcal{PT}$ symmetry, the universal quantum work relation does not hold because the norm is not preserved during the dynamics.