Gauge Quantum Thermodynamics of Time-local non-Markovian Evolutions

Dealing with a generic time-local non-Markovian master equation, currents and power are defined to be process-dependent as in classical thermodynamics. Each process is characterized by a symmetry transformation, a gauge of the quantum master equation, and is associated to different amounts of heat and/or work. Once the thermodynamical quantities are fixed by the symmetry requirement, a consistent interpretation of the laws of thermodynamics emerges. We also provide necessary and sufficient conditions for a system to have a gauge-independent thermodynamical description.