Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics

TL;DR

This paper introduces weighted reciprocal temperature and weighted thermal flux concepts to unify thermodynamic fluxes and forces, analyzing efficiency at maximum power in finite-time heat engines and refrigerators with universal features.

Contribution

It proposes new weighted thermodynamic quantities and applies them to derive universal efficiency results in finite-time thermodynamics.

Findings

Efficiency at maximum power matches low-dissipation engine results

Mappings for typical engines like Feynman ratchet are constructed

Universal efficiency up to quadratic order is established for symmetric coupling

Abstract

The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, {Phys. Rev. Lett.} \textbf{105}, 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.