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  • Letter
  • Open Access

Violation of local detailed balance upon lumping despite a clear timescale separation

David Hartich* and Aljaž Godec†

  • Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany

  • *david.hartich@mpinat.mpg.de
  • †agodec@mpinat.mpg.de
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Phys. Rev. Research 5, L032017 – Published 7 August, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032017

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 timescale separation local detailed balance is believed to inherently 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 lumping leads to a violation of local detailed balance despite a clear timescale 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 as far as we know 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.

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Outline

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Phys. Rev. Research 5, L032017– Published 7 August, 2023
  • Received 23 November 2021
  • Accepted 21 June 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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