Time-Resolved Statistics of Snippets as General Framework for Model-Free Entropy Estimators.

Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time reversal like a current. We introduce a general framework that allows us to infer a lower bound on entropy production through measuring the time-resolved statistics of events with any symmetry under time reversal, in particular, time-symmetric instantaneous events. We emphasize Markovianity as a property of certain events rather than of the full system and introduce an operationally accessible criterion for this weakened Markov property. Conceptually, the approach is based on snippets as particular sections of trajectories between two Markovian events, for which a generalized detailed balance relation is discussed.

Waiting Time Distributions in Hybrid Models of Motor-Bead Assays: A Concept and Tool for Inference.

In single-molecule experiments, the dynamics of molecular motors are often observed indirectly by measuring the trajectory of an attached bead in a motor-bead assay. In this work, we propose a method to extract the step size and stalling force for a molecular motor without relying on external control parameters. We discuss this method for a generic hybrid model that describes bead and motor via continuous and discrete degrees of freedom, respectively. Our deductions are solely based on the observation of waiting times and transition statistics of the observable bead trajectory. Thus, the method is non-invasive, operationally accessible in experiments and can, in principle, be applied to any model describing the dynamics of molecular motors. We briefly discuss the relation of our results to recent advances in stochastic thermodynamics on inference from observable transitions. Our results are confirmed by extensive numerical simulations for parameters values of an experimentally realized F1-ATPase assay.

Operationally accessible uncertainty relations for thermodynamically consistent semi-Markov processes.

Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium imposes a crucial condition called direction-time independence for which we present an alternative derivation. We prove a thermodynamic uncertainty relation that formally resembles the one for a discrete-time Markov process. The result relates the entropy production of the semi-Markov process to mean and variance of steady-state currents. We prove a further thermodynamic uncertainty relation valid for semi-Markov descriptions of coarse-grained Markov processes that emerge by grouping states together. A violation of this inequality can be used as an inference tool to conclude that a given semi-Markov process cannot result from coarse graining an underlying Markov one. We illustrate these results with representative examples.