TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.9.3.030
TI  - Sustaining a temperature difference
PY  - 2020/09/02
UR  - https://scipost.org/SciPostPhys.9.3.030
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 9
IS  - 3
SP  - 030
A1  - Polettini, Matteo
AU  - Garilli, Alberto
AB  - We derive an expression for the minimal rate of entropy that sustains two reservoirs at different temperatures $T_0$ and $T_\ell$. The law displays an intuitive $\ell^{-1}$ dependency on the relative distance and a characterisic $\log^2 (T_\ell/T_0)$ dependency on the boundary temperatures. First we give a back-of-envelope argument based on the Fourier Law (FL) of conduction, showing that the least-dissipation profile is exponential. Then we revisit a model of a chain of oscillators, each coupled to a heat reservoir. In the limit of large damping we reobtain the exponential and squared-log behaviors, providing a self-consistent derivation of the FL. For small damping "equipartition frustration" leads to a well-known balistic behaviour, whose incompatibility with the FL posed a long-time challenge.
ER  -

@Article{10.21468/SciPostPhys.9.3.030,
	title={{Sustaining a temperature difference}},
	author={Matteo Polettini and Alberto Garilli},
	journal={SciPost Phys.},
	volume={9},
	pages={030},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.9.3.030},
	url={https://scipost.org/10.21468/SciPostPhys.9.3.030},
}