Operational meaning of generalized temperatures in a Carnot-like nonequilibrium engine

Investigate whether the generalized temperatures TH and Tc used to define isothermal segments and the efficiency bound of the proposed Carnot-like cyclic engine can be interpreted as reservoir (bath) temperatures rather than merely integrated properties of the system maintained by protocol design; establish criteria under which these temperatures have an operational bath-level meaning in irreversible nonequilibrium processes.

Background

In the Supplemental Material, the authors construct a Carnot-like cycle using the generalized temperature T to define isothermal and adiabatic steps, deriving an efficiency expression that reduces to the classical Carnot bound when irreversible contributions vanish.

They note that, unlike classical thermodynamics where the temperatures in the Carnot bound are those of the two baths, here T is a system-defined quantity that depends on the protocol and dynamics. The authors explicitly state that it remains to be explored whether the temperatures appearing in their efficiency expression possess a robust operational interpretation beyond being integrated system properties.