A large deviation analysis on the near-equivalence between external and internal reservoirs

• Mapping external into internal reservoirs can yield equivalent entropy production.
• Only heat fluctuation can distinguish an external from an internal reservoir.
• The best approximation to coloured reservoirs is its white-noise analogue.

Within the spirit of van Kampen’s “Langevin approach”, we discuss the limits of validity of rephrasing the non-equilibrium problem of a particle subject to an external (work) reservoir–a system where the fluctuation–dissipation relation is not verified–into the simpler case with an internal (heat) reservoir for which the fluctuations and the dissipation arise from the same source. Using a convenient mapping of the thermomechanical parameters we show that, counter-intuitively, such approach is not only valid for steady state time independent quantities, but also for time dependent thermostatistical quantities, namely the injected and dissipated fluxes. We connect this result with the problem of large deviations and conclude that, in this context, we can only distinguish reservoirs by analysing the “fluctuations of accumulated fluctuations”. As a by-product, we learn that the best reference approximation to the large deviation functions of a non-Markovian external reservoir system is not the respective internal reservoir limit–as often assumed and suggested by the Langevin approach–but its internal reservoir analogue system obtained from the mapping of the original thermomechanical parameters.