Engines with ideal efficiency and nonzero power for sublinear transport laws

TL;DR

This paper demonstrates theoretically that engines with nonzero power can achieve ideal efficiency by replacing linear transport laws with sublinear ones and considering a step-function limit, without violating thermodynamic inequalities.

Contribution

It introduces a novel approach using sublinear transport laws and step-function limits to realize ideal efficiency at nonzero power in engines.

Findings

Achieves ideal efficiency with nonzero power through sublinear transport laws.

Maintains thermodynamic inequalities in the step-function limit.

Provides a theoretical framework for high-efficiency engines.

Abstract

It is known that an engine with ideal efficiency ($\eta =1$ for a chemical engine and $e = e_{\rm Carnot}$ for a thermal one) has zero power because a reversible cycle takes an infinite time. However, at least from a theoretical point of view, it is possible to conceive (irreversible) engines with nonzero power that can reach ideal efficiency. Here this is achieved by replacing the usual linear transport law by a sublinear one and taking the step-function limit for the particle current (chemical engine) or heat current (thermal engine) versus the applied force. It is shown that in taking this limit exact thermodynamic inequalities relating the currents to the entropy production are not violated.