Violation of Local Detailed Balance Despite a Clear Time-Scale Separation

TL;DR

This paper demonstrates that local detailed balance can be violated in Markov models of molecular motors despite clear time-scale separation, and shows that Milestoning can restore thermodynamic consistency even with memory effects.

Contribution

It provides a clear example where local detailed balance fails despite time-scale separation and establishes Milestoning as a thermodynamically consistent coarse-graining method.

Findings

Local detailed balance can be violated despite Markovian dynamics.

Milestoning restores local detailed balance even with memory effects.

The work highlights the importance of coarse-graining choices for thermodynamic consistency.

Abstract

Integrating out fast degrees of freedom is known to yield, to a good approximation, memory-less, i.e. Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee thermodynamic consistency arbitrarily far from equilibrium. Here we present a transparent example of a Markov model of a molecular motor where local detailed balance can be violated despite a clear time-scale separation and hence Markovian dynamics. Driving the system far from equilibrium can lead to a violation of local detailed balance against the driving force. We further show that local detailed balance can be restored, even in the presence of memory, if the coarse-graining is carried out as Milestoning. Our work establishes Milestoning not only as a kinetically but for the first time also as a thermodynamically consistent coarse-graining method. Our results are relevant as soon as individual transition paths are appreciable or can be resolved.