Inferences from transition statistics of partial information

The rapidly growing field of Stochastic Thermodynamics relies on the mathematics of Markov processes to assess Statistical Physics concepts outside of thermal equilibrium, it thrives under the full knowledge of the microscopic dynamics via master or Fokker-Planck equations. However, in most realistic settings, part of the information is hidden, what in fact distinguishes Statistical Mechanics from Thermodynamics is that for the latter only macroscopic phenomena are available.

Some recent works address the issue of partial information by considering a specific set of observable states [1,2]. Conversely, in this work we consider that a set of transitions are the only observables. Molecular machines represent one of the biggest examples of such setting [3], their internal state and most transitions are hidden (e.g. dynein's consumption of one ATP), however some specific transitions are observable (e.g. dynein's steps along a microtubule).

From Stochastic Thermodynamics and first-passage-time techniques we derive analytical expressions to characterize such transitions that strikingly describe data from simulations [4]. We address how the observer can make inferences about irreversibility, disorder and topology of an underlying process from the collected partial information. Lastly, we compare our results to simulations of biophysics-inspired systems.

[1] M Polettini and M Esposito. PRL 119.24 (2017): 240601.

[2] IA Martínez, G Bisker, JM Horowitz, and JM Parrondo. Nature communications 10.1 (2019): 1-10.

[3] YR Chemla, JR Moffitt, and C Bustamante.  J. Phys. Chem. B 112.19 (2008): 6025-6044.

[4] PE Harunari, A Dutta, É Roldán, and M Polettini. Work in preparation.