Finite-time and first-passage analysis of the multicyclic chemo–thermal motor

Investigate how long the productive mechanical ring takes to complete a winding and how the attached futile chemical ring reshapes the corresponding first-passage-time distribution, thereby extending the exactly solvable multicyclic chemo–thermal motor to finite-time and first-passage regimes.

Background

The paper introduces a five-state figure-eight network consisting of a productive three-state mechanical cycle and an attached three-state futile chemical loop that share one state. At mechanical stall, the productive cycle has zero current while the futile cycle can continue consuming fuel and generating entropy. This establishes a minimal model of hidden dissipation in an idling molecular motor.

The authors identify finite-time and first-passage properties as unresolved extensions of this model. In particular, they leave open the duration required for a productive-ring winding and the influence of the futile chemical cycle on the distribution of those completion times. These questions would connect the exact steady-state thermodynamic analysis to transient transport and stochastic timing behavior.

References

The same figure-eight topology, in which one ring carries a mechanical current while an attached ring turns over chemically, is the natural starting point for finite-time and first-passage questions---how long the productive ring takes to complete a winding, and how the futile ring reshapes that distribution---which have been studied for related stochastic systems and for time-dependent driving of Brownian engines . We leave such extensions of the present exactly solvable model to future work.

— Exact chemo--thermal Metropolis Brownian engine: chemical leverage, temperature-neutral stall, power optimization, and multicyclic dissipation  (2608.25638 - Taye, 26 Aug 2026) in Section Discussion