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

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.

arXiv comment12 pages, 5 figures. Minor corrections and new Supplemental Material

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