Thermodynamic bounds and error correction for faulty coarse graining

TL;DR

This paper introduces a new approach to coarse graining in stochastic thermodynamics that accounts for observation errors, providing bounds on entropy production and methods for error correction in nanoscale systems.

Contribution

It develops a framework for coarse graining with errors that preserves thermodynamic consistency and derives bounds relating error sensitivity to system driving.

Findings

Error-structured coarse graining can keep observed entropy production consistent with true values.

Thermodynamic bounds relate error sensitivity to network driving strength.

Redundancy in observations enables error detection and correction.

Abstract

At the nanoscale, random effects govern not only the dynamics of a physical system but may also affect its observation. This work introduces a novel paradigm for coarse graining that eschews the assignment of a unique coarse-grained trajectory to a microscopic one. Instead, observations are not only coarse-grained but are also accompanied by a small chance of error. Formulating the problem in terms of path weights, we identify a condition on the structure of errors that ensures that the observed entropy production does not increase. As a result, the framework of stochastic thermodynamics for estimating entropy production can be extended to this broader class of systems. As an application, we consider Markov networks in which individual transitions can be observed but may be mistaken for each other. We motivate, derive, and illustrate thermodynamic bounds that relate the error sensitivity of the observed entropy production to the strength of the driving and are valid for arbitrary network topologies. If sufficiently many transitions in the network can be observed, redundancies in the coarse-grained trajectories can be used to detect and correct errors, which potentially improves naive estimates of entropy production. We conclude with an outlook on subsequent research on thermodynamic bounds for erroneous coarse graining.