Gauge Quantum Thermodynamics of Time-local non-Markovian Evolutions

Dealing with a generic time-local non-Markovian master equation, we define current and power to be process-dependent as in classical thermodynamics. Each process is characterized by a symmetry transformation, a gauge of the master equation, and is associated with different amounts of heat and/or work. Once the symmetry requirement fixes the thermodynamical quantities, a consistent gauge interpretation of the laws of thermodynamics emerges. We also provide the necessary and sufficient conditions for a system to have a gauge-independent thermodynamical behavior and show that systems satisfying Quantum Detailed Balance conditions are gauge-independent. Applying the theory to quantum thermal engines, we show that gauge transformations can change the machine efficiency, however, yet constrained by the classical Carnot bound.