Abstract
We study the phenomenology of maximum-entropy meso-reservoirs, where we assume that their local thermal equilibrium state changes consistently with the heat transferred between the meso-reservoirs. Depending on heat and matter carrying capacities, the chemical potentials and temperatures are allowed to vary in time, and using global conservation relations we solve their evolution equations. We compare two-terminal transport between bosonic and fermionic meso-reservoirs via systems that tightly couple energy and matter currents and systems that do not. For bosonic reservoirs, we observe the temporary formation of a Bose–Einstein condensate in one of the meso-reservoirs from an initial nonequilibrium setup.
Highlights
A reservoir is treated as constant and inert to all systems that are coupled to it [1, 2]
In particular in nonequilibrium setups, small systems may in the long-run transfer a significant amount of heat, and it may no longer be applicable to talk about a constant reservoir temperature or chemical potential [14, 15, 16, 17, 5, 18]
Meso-Reservoir Dynamics In Fig. 2 we show the relaxation dynamics of the temperatures and chemical potentials for two fermionic reservoirs in the wideband limit coupled via two non-interacting quantum dots
Summary
A reservoir is treated as constant and inert to all systems that are coupled to it [1, 2]. In particular in nonequilibrium setups (e.g. realized by periodic driving or by locally different thermal states), small systems may in the long-run transfer a significant amount of heat, and it may no longer be applicable to talk about a constant reservoir temperature or chemical potential [14, 15, 16, 17, 5, 18]. Where β(t) = 1/T (t) and μ(t) are time-dependent inverse temperature and chemical potential of the meso-reservoir, and HMR and NMR denote Hamiltonian and particle number operator of the meso-reservoir At this maximum entropy state, the internal entropy production of the meso-reservoir vanishes [30], and the change of its entropy is solely governed by the heat transfer S → SD = β(t)[JE − μ(t)JM ], quantified by the energy current JE and matter current JM entering the meso-reservoir via the system.
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