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.

Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

“…Upon application to the kinetic scheme in Figure (top left), states 2 and 3 that constitute compound state B could be lumped together and the scheme could be reduced to the two-state scheme (Figure , bottom) if the 2 ⇄ 3 interconversion dynamics within B is fast. However, the detailed balance may still be violated by the full kinetic model, while it is not violated by the reduced two-state model; in this case, the irreversibility of the true dynamics is hidden from observation . We will see another example of this kind in Experimental Limitations in Transition-Path Measurements.…”

Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states

“…For systems that are weakly coupled to an environment in thermal equilibrium, the entropy production rate equals the dissipation rate [17,19,27], which clarifies the physical significance of the process S(t). In the literature, the latter property is often referred to as the principle of local detailed balance [28,29].…”

Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining

“…[72][73][74][75] Applied to a second-order semi-Markov process, this KLD estimator of the EPR breaks into two contributions, 64 the affinity EPR, EPR aff , which accounts for the net flux and affinity or the thermodynamic force, 68,70 and the waiting-time-distribution (WTD) EPR, EPR WTD , which accounts for the broken time-reversal symmetry in the waiting time distributions. 64 For second-order semi-Markov processes, which naturally emerge when ''lumping'' adjacent states, 64,76 the EPR WTD can provide a lower bound on the total EPR, even when the system does not have any net current observed and EPR aff = 0. Describing processes by transitions instead of states, 77 the KLD estimator for the EPR was further applied to waiting times in between observed transitions.…”

“…In a recent study, using a Markovian model of a driven molecular motor, Hartich et al compared different coarse-graining schemes, ''milestoning'' and ''lumping'', and found that the ''milestoning'' method can restore Markovian dynamics in the case of timescale separation and preserves local detailed balance. 76,86 The quantitative effect of the coarse-graining on the EPR was estimated in an experimental system of steady-state trajectories of a microtubule length using an optimization procedure of a two-step estimator, where it was demonstrated that increasing the spatial and temporal resolution while coarse-graining leads to an improved EPR bound. 79 Moreover, a recent study by Tan et al 95 has found that the time-irreversibility varies nonmonotonically with the lag time, i.e., the time intervals between the position measurements, which determines the dissipation timescale.…”

“…In a recent study, using a Markovian model of a driven molecular motor, Hartich et al compared different coarse-graining schemes, “milestoning” and “lumping”, and found that the “milestoning” method can restore Markovian dynamics in the case of time-scale separation and preserves local detailed balance. 76 , 86 …”