Hidden symmetries and nonlinear constitutive relations for tight-coupling heat engines

TL;DR

This paper reveals hidden symmetries in heat engines that lead to a unified nonlinear relation for their heat exchanges and flows, advancing the theoretical understanding of thermodynamic processes.

Contribution

It introduces a generic nonlinear constitutive relation for tight-coupling heat engines based on identified hidden symmetries, extending previous linear models.

Findings

Derived quadratic-order nonlinear relations for cyclic heat engines.

Established duality of heat exchanges under symmetry transformations.

Unified description for autonomous heat engines based on symmetries.

Abstract

Typical heat engines exhibit a kind of homotypy: The heat exchanges between a cyclic heat engine and its two heat reservoirs abide by the same function type; the forward and backward flows of an autonomous heat engine also conform to the same function type. This homotypy mathematically reflects in the existence of hidden symmetries for heat engines. The heat exchanges between the cyclic heat engine and its two reservoirs are dual under the joint transformation of parity inversion and time-reversal operation. Similarly, the forward and backward flows in the autonomous heat engine are also dual under the parity inversion. With the consideration of these hidden symmetries, we derive a generic nonlinear constitutive relation up to the quadratic order for tight-coupling cyclic heat engines and that for tight-coupling autonomous heat engines, respectively.