Criteria for fluctuating-temperature versus non-equilibrium descriptions of finite-size reservoirs

Determine precise physical conditions under which a finite-size thermal reservoir coupled to a quantum system can be effectively modeled by a fluctuating temperature, and identify when a full non-equilibrium description is required, thereby delineating the boundary between these two modeling regimes for finite-size environments.

Background

The lecture notes emphasize that quantum thermodynamics often models environments as large and memoryless, characterized by fixed temperatures and chemical potentials. Recent experiments and theoretical developments have highlighted scenarios where reservoirs are finite and may exhibit temperature fluctuations or develop significant non-equilibrium features.

Several approaches have been proposed to describe such cases, including extended micro-canonical master equations that track bath energy dynamics and descriptions of energy exchanges between arbitrary quantum systems. Results for specific models (e.g., a single-level quantum dot coupled to a finite-size reservoir) suggest that an "entropic temperature" can characterize system equilibration, but a general criterion for when this is appropriate remains unsettled.

The authors explicitly identify the need to establish when a fluctuating-temperature description suffices and when a non-equilibrium framework is necessary, marking this as an open question within the broader effort to understand finite-size environments and their thermodynamic behavior.