Efficiency at maximum power of thermochemical engines with near-independent particles

TL;DR

This paper analyzes the efficiency at maximum power of thermochemical engines using near-independent particles, introducing an energy filter to control flux coupling, and derives bounds related to Carnot and Curzon-Ahlborn efficiencies.

Contribution

It provides a theoretical framework for understanding efficiency bounds of thermochemical engines with different particle statistics and a novel energy filter mechanism.

Findings

Efficiency decreases monotonically with filter width.

Efficiency bounds are related to Carnot efficiency, with specific bounds for Bose-Einstein systems.

Maximum power scales with the square of temperature difference.

Abstract

Two-reservoir thermochemical engines are established in by using near-independent particles (including Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein particles) as the working substance. Particle and heat fluxes can be formed based on the temperature and chemical potential gradients between two different reservoirs. A rectangular-type energy filter with width $\Gamma$ is introduced for each engine to weaken the coupling between the particle and heat fluxes. The efficiency at maximum power of each particle system decreases monotonously from an upper bound $\eta^+$ to a lower bound $\eta^-$ when $\Gamma$ increases from 0 to $\infty$. It is found that the $\eta^+$ values for all three systems are bounded by $\eta_{\mathrm{C}}/2 \leq \eta^+ \leq \eta_{\mathrm{C}}/(2-\eta_{\mathrm{C}})$ due to strong coupling, where $\eta_{\mathrm{C}}$ is the Carnot efficiency. For the Bose-Einstein system, it is found that the upper bound is approximated by the Curzon-Ahlborn efficiency: $\eta_{\mathrm{CA}}=1-\sqrt{1-\eta _{\mathrm{C}}}$. When $\Gamma\rightarrow\infty$, the intrinsic maximum powers are proportional to the square of the temperature difference of two reservoirs for all three systems, and the corresponding lower bounds of efficiency at maximum power can be simplified in the same form of $\eta^{-}=\eta_{\mathrm{C}}/[1+a_0(2-\eta_{\mathrm{C}})]$.