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Experimentally Accessible Measurement of Irreversibility in Stochastic Systems by Categorizing Single-Molecule Displacements

Alvaro Lanza1, Inés Martínez-Martín1, Rafael Tapia-Rojo1,2, and Stefano Bo1,2

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Phys. Rev. X 16, 031052 – Published 26 August, 2026

DOI: https://doi.org/10.1103/j3jk-k315

Abstract

Quantifying the irreversibility and dissipation of nonequilibrium processes is crucial to understanding their behavior, assessing their possible capabilities, and characterizing their efficiency. We introduce a physical quantity that quantifies the irreversibility of stochastic Langevin systems from the observation of individual molecules’ displacements. Categorizing these displacements into a few groups based on their initial and final positions allows us to measure irreversibility precisely without the need to know the forces and magnitude of the fluctuations acting on the system. For short times, our model-free estimate of irreversibility is related to entropy production by a conditional fluctuation theorem. For short times and, in general, for stationary protocols, our estimate provides a lower bound to the average entropy production. We validate the method on single-molecule force spectroscopy experiments of proteins subject to force ramps. We show that irreversibility is sensitive to detailed features of the energy landscape underlying the protein folding dynamics and suggest how our methods can be employed to unveil key properties of protein folding processes.

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Irreversibility and dissipation are hallmarks of nonequilibrium systems such as artificial engines, molecular motors, and biomolecular transitions. Quantifying how far systems are from thermodynamic equilibrium characterizes their function and efficiency, but remains notoriously difficult in small stochastic systems, such as single biomolecules under force. We propose a method to measure irreversibility directly from single-molecule recordings, without needing an estimation of the forces or diffusion coefficient. One simply records the initial and final positions of particles in a time window and categorizes their displacements into different classes, based on where they start and end. We applied our method to nonequilibrium protein pulling experiments to obtain a detailed time-dependent evaluation of irreversibility in the unfolding and refolding process. This offers direct insight into the folding mechanism of two different mechanosensitive proteins. Our results provide a versatile and accessible tool to characterize and interpret small systems in terms of irreversibility for time-dependent, continuous, nonequilibrium dynamics.

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Phys. Rev. X 16, 031052– Published 26 August, 2026
  • Received 2 December 2025
  • Accepted 14 July 2026
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