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 ηmp takes the form $1/2+c \,\Delta \mu + {\cal O}(\Delta \mu ^2)$, with 1/2 a universal constant and Δμ 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 ηmp is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model, we obtain ηmp = 1/(θ + 1), with θ > 0 the power of Δμ in the transport equation.
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Although an explicit model for realizing anomalous transport laws is outside the scope of our present paper, we briefly sketch some possibilities. On the one hand, in order to obtain a vanishing linear transport coefficient (or even a negative one) we consider a system that is brought out of equilibrium due to a driving force (e.g., originating from an electric field). On top of this driving force, we consider particle transport in response to a chemical potential difference. Under such circumstances, the (Green-Kubo-like) relation between the linear transport coefficient and the correlation function time-integral is modified, and the former need not be positive anymore. A vanishing of the linear coefficient would then provide a system for which higher than first-order terms in the transport law are dominant. On the other hand, the somewhat more familiar situation of a diverging linear transport coefficient (e.g., akin to a static susceptibility or compressibility at a bulk critical point) is symptomatic of the presence of sublinear terms in the transport law, leading to a model with θ < 1 in our notation.
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