Coarse-Graining via Lumping: Exact Calculations and Fundamental Limitations

TL;DR

This paper introduces a lumping method for semi-Markov models that accurately reproduces entropy-production statistics of microscopic dynamics, enabling better inference of nonequilibrium properties despite limited state resolution.

Contribution

The authors develop an exact coarse-graining technique that preserves entropy production statistics and reveals fluctuation theorem violations in semi-Markov models.

Findings

Mean entropy production remains accurate after lumping.

Higher-order information may be lost during coarse-graining.

The method captures fluctuation theorem violations consistent with experiments.

Abstract

Detecting broken time-reversibility at micro- and nanoscale is often difficult when experiments offer limited state resolution. We introduce a lumping method that builds an effective semi-Markov model able to reproduce exactly the full entropy-production statistics of the microscopic dynamics. The mean entropy production stays accurate even when hidden current-carrying cycles are merged, though higher-order information can be unavoidably lost. In these cases, we capture violations of fluctuation theorems consistent with experiments, opening a path to novel inference strategies out of equilibrium.