Efficiency at maximum power of a chemical engine

TL;DR

This paper analyzes the efficiency at maximum power of a cyclic chemical engine converting chemical to mechanical energy, revealing universal and non-universal behaviors depending on the transport law and symmetry properties.

Contribution

It derives a general form for efficiency at maximum power, showing universality at linear order and non-universality under certain nonlinear transport modifications.

Findings

Efficiency at maximum power is 1/2 + c Δμ + O(Δμ^2) with universal leading term.

The coefficient c is zero for symmetric or antisymmetric fluxes.

Nonlinear transport models yield efficiency η = 1/(θ+1), depending on the transport law.

Abstract

A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law for particle uptake and release, the efficiency at maximum power $\eta$ takes the form 1/2+c\Delta \mu + O(\Delta \mu^2), with 1/2 a universal constant and $\Delta \mu$ the chemical potential difference between the particle reservoirs. The linear coefficient c is zero for engines featuring a so-called left/right symmetry or particle fluxes that are antisymmetric in the applied chemical potential difference. Remarkably, the leading constant in $\eta$ is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model we obtain \eta = 1/(\theta +1), with \theta >0 the power of $\Delta \mu$ in the transport equation