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Sustaining a temperature difference

by Matteo Polettini, Alberto Garilli

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Submission summary

Authors (as registered SciPost users): Alberto Garilli · Matteo Polettini
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-08-20
Date submitted: 2020-08-04 13:21
Submitted by: Garilli, Alberto
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


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.

List of changes

- We added some additional references [15,23,29]
- The typos have been corrected. In particular the definition of the thermodynamic forces $F_{k h}$ under eq. 26
- Some further explanations on some passages have been added and labelled in red
- We corrected some labelling in the main text and in the appendices
- We changed fig. 4 with a better picture so that it is clearer than before
- We added the condition $p_0$ = 0 among the conditions of non-oscillating endpoints
- We added a missing parenthesis in eq. 18

Published as SciPost Phys. 9, 030 (2020)

Reports on this Submission

Anonymous Report 2 on 2020-8-13 (Invited Report)


The authors gave satisfactory answers to my comments. I recommend the manuscript for publication.

  • validity: top
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2020-8-4 (Invited Report)


I am satisfied with the authors' changes and recommend the manuscript for publication.

(please note a small typo on p9, kind -> kind of)

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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