Irreversible efficiency and Carnot theorem for heat engines operating with multiple heat baths in linear response regime

Abstract

The Carnot theorem, one expression of the second law of thermodynamics, places a fundamental upper bound on the efficiency of heat engines operating between two heat baths. The Carnot theorem can be stated in a more generalized form for heat engines operating with multiple heat baths, where the maximum efficiency is achieved for reversible heat engines operating quasistatically between two heat baths. In this study, we determine the irreversible efficiency of general heat engines operating in a linear response regime by quantifying the impact of the dissipation by irreversible operations. The generalized Carnot theorem is derived as a natural consequence of it. Because the result obtained is based on the linear response relation and fluctuation-dissipation theorem in the universal framework of linear response theory, it has wide applicability to heat engines operating in the linear response regime.

Relation between fluctuations and efficiency at maximum power for small heat engines

“…(2) MP and minimizing the fluctuation of work output for the finite-time heat engines are interesting open problems. Also, thermodynamic geometry [25,26,58,[75][76][77][78] is a good method leads to further studies on the properties of η (2) .…”

“…In the framework of endoreversible thermodynamics, the finite-time heat engines are usually characterized by the performance at maximum power. For example, the efficiency at maximum power (EMP), η MP , is an important quantity which has been studied for various kinds of small heat engines [52][53][54][55][56][57][58]. Therefore, it is natural to ask what is the fluctuation of performance at maximum power.…”