CYNAR: a trajectory-based estimator of entropy production
Abstract
Inferring the entropy production rate σ from recorded trajectories is a key challenge in stochastic thermodynamics. In experiments, the forces governing the dynamics are usually unknown and often only some of the system's degrees of freedom can be observed. Building on a recently introduced method [I. Di Terlizzi, Phys. Rev. Lett. 135, 237101 (2025)], we develop and validate CYNAR (computation yields nonequilibrium analysis and reconstruction), a pipeline that estimates σ from trajectories. It exploits a kinetic decomposition of σ into a traffic term cal T, inferred from the short-time curvature of correlation functions, and an inflow rate cal G, computed from the steady-state score, i.e., the gradient of the log-density. We show that the same decomposition, evaluated on any subset of observed coordinates, always bounds σ from below, for any diffusion tensor and without knowledge of the hidden degrees of freedom. We then compare CYNAR with a more standard approach that estimates σ from steady-state probability currents, on four systems of increasing complexity. CYNAR proves to be more reliable, with no detectable bias close to equilibrium, weak dependence on spatial discretization, and marked robustness to measurement noise. It is also readily applicable to high-dimensional systems, where the traffic alone provides a lower bound close to σ, and remains informative under partial observation, including cases where the flux-based estimate vanishes identically. CYNAR is provided as an open-source Python package.
Related
- Wasserstein-2 gradient flows and the geometry of entropy production in classical and quantum stochastic thermodynamics
- Partial Entropy production of active particles with hidden states in potentials
- Second largest eigenvalue does not bound stationary entropy production
- Lower bounds on entropy production from dynamical correlation functions
- Entropy Production in Mesoscopic Electronic Transport Beyond Weak-Coupling
BibTeX
@misc{baiesi2026cynar,
title = {{CYNAR: a trajectory-based estimator of entropy production}},
author = {Marco Baiesi and Ivan DI Terlizzi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39654},
eprint = {2609.39654},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39654},
}
RIS
TY - UNPB
TI - CYNAR: a trajectory-based estimator of entropy production
AU - Marco Baiesi
AU - Ivan DI Terlizzi
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.39654
UR - https://arxiv.org/abs/2609.39654
AB - Inferring the entropy production rate σ from recorded trajectories is a key challenge in stochastic thermodynamics. In experiments, the forces governing the dynamics are usually unknown and often only some of the system's degrees of freedom can be observed. Building on a recently introduced method [I. Di Terlizzi, Phys. Rev. Lett. 135, 237101 (2025)], we develop and validate CYNAR (computation yields nonequilibrium analysis and reconstruction), a pipeline that estimates σ from trajectories. It exploits a kinetic decomposition of σ into a traffic term cal T, inferred from the short-time curvature of correlation functions, and an inflow rate cal G, computed from the steady-state score, i.e., the gradient of the log-density. We show that the same decomposition, evaluated on any subset of observed coordinates, always bounds σ from below, for any diffusion tensor and without knowledge of the hidden degrees of freedom. We then compare CYNAR with a more standard approach that estimates σ from steady-state probability currents, on four systems of increasing complexity. CYNAR proves to be more reliable, with no detectable bias close to equilibrium, weak dependence on spatial discretization, and marked robustness to measurement noise. It is also readily applicable to high-dimensional systems, where the traffic alone provides a lower bound close to σ, and remains informative under partial observation, including cases where the flux-based estimate vanishes identically. CYNAR is provided as an open-source Python package.
ER -