Characterizing work fluctuations in non-Hermitian dynamics of a superconducting qubit

In quantum systems, work fluctuations can be determined through pairs of projective energy measurements on an ensemble. The resulting work distribution can be related to the equilibrium free energy change by the Jarzynski equality. However, for open quantum systems, the equality may require modifications. Here we study the validity of the equality in non-Hermitian dynamics of a superconducting qubit, where an effective non-Hermitian Hamiltonian is realized on a sub-manifold of states of a dissipative transmon circuit. We show that the Jarzynski equality remains valid for dynamics confined to parameter regions with effective parity-time symmetry, where the system eigenenergies remain real. Outside these regions, the complex energy spectrum results in a violation of the equality. Characterization of this violation forms the basis for an extension of the Jarzynski equality for non-Hermitian dynamics, where complex energy evolution can be related to changes in information.