Work statistics in effective non-Hermitian systems*

Non-Hermitian systems with specific forms of Hamiltonians can exhibit novel phenomena, but often such systems are hard to realize, especially in the quantum regime. A proper description of these difficulties can help to introduce optimizing methods. Thermodynamic quantities can be potential choices, but the present thermodynamics theory does not work well in non-Hermitian systems. We treat non-Hermitian systems as effective processes generated from Hermitian systems, so that the free energy cost of these processes can be studied from the work statistics. A way to define the work statistics in such non-Hermitian systems is also provided. Based on these results, we further show an example of optimized process to generate a non-Hermitian system.