Reconstruction of Markovian dynamics from untimed data

TL;DR

This paper presents a theoretical framework for inferring Markovian nonequilibrium dynamics from incomplete, untimed snapshot data, emphasizing the reconstruction of temporal information before deriving equations of motion.

Contribution

It introduces a method to reconstruct time and dynamics from macrostate snapshots without timing information, advancing analysis of irreversible Markovian processes.

Findings

Framework successfully infers dynamics from untimed data

Reconstruction of time enables accurate equations of motion

Applicable to genuinely irreversible Markovian systems

Abstract

I develop a theoretical framework for inferring nonequilibrium equations of motion from incomplete experimental data. I focus on genuinely irreversible, Markovian processes, for which the incomplete data are given in the form of snapshots of the macrostate at different instances of the evolution, yet without any information about the timing of these snapshots. A reconstruction of the equation of motion must therefore be preceded by a reconstruction of time.