Direction of heat flow between two nonequilibrium systems characterized by the generalized temperature T

Ascertain whether the generalized temperature T, defined for Markovian overdamped Langevin systems that violate the Einstein relation as a system-level variable linking average calorimetric heat dissipation to average informatic entropy production, determines the direction of net heat flow when two such systems are brought into contact; specifically, establish whether heat necessarily flows from the system with higher T to the one with lower T under physically reasonable coupling conditions.

Background

The paper introduces a generalized temperature T for nonequilibrium Langevin systems where the Einstein relation between mobility and diffusivity fails. This T restores a second-law-like inequality at the level of averages, re-establishing a correspondence between informatic entropy production and thermodynamic dissipation, and enabling analogues of classical thermodynamic results.

In equilibrium thermodynamics, temperature determines the direction of heat flow between systems (zeroth-law intuition). The authors show that their generalized T dictates the sign of heat flow into or out of a single system based on entropy change but explicitly raise the question of whether T also controls heat flow direction between two systems when they interact, leaving this point unresolved.