https://doi.org/10.1140/epjp/s13360-025-07181-4
Tutorial
Fluctuation theorems with optical tweezers: theory and practice
1
Instituto de Física de São Carlos, Universidade de São Paulo, IFSC – USP, 13566-590, São Carlos, SP, Brazil
2
International Centre for Theory of Quantum Technologies, University of Gdańsk, Jana Bażyńskiego 1A, 80-309, Gdańsk, Poland
3
Instituto de Física ‘Gleb Wataghin’, Universidade Estadual de Campinas, 13083-859, Campinas, SP, Brazil
4
ENS de Lyon, CNRS, Laboratoire de Physique, Université de Lyon, 69342, Lyon, France
5
CNRS, institut Lumière Matière, UMR 5306, Université Claude Bernard Lyon 1, 69100, Villeurbanne, France
a
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Received:
31
October
2025
Accepted:
6
December
2025
Published online:
24
January
2026
Abstract
Fluctuation theorems, such as the Jarzynski equality and the Crooks relation, are effective tools connecting non-equilibrium work statistics and equilibrium free energy differences. However, detailed hands-on, reproducible protocols for implementing and analyzing these relations in real experiments remain scarce. This tutorial provides an end-to-end workflow for measuring, validating, and applying fluctuation theorems using a single-beam optical tweezers setup. It introduces the foundational ideas and consolidates practical calibration (PSD-based trap stiffness and position sensitivity), protocol design (forward/reverse finite-time drives over multiple amplitudes and durations), and robust estimators for free energy difference and dissipated work, highlighting finite sampling and rare event effects. We demonstrate the procedures using an extensive set of measured trajectories under different conditions and provide openly accessible datasets and Python code, enabling new researchers or educators to reproduce the results with minimal effort. Beyond pedagogical validation, we discuss how these recipes translate to broader soft-matter and mesoscopic contexts. By combining user-friendly instruments with clear and transparent analysis, this work promotes the education and reliable adoption of stochastic thermodynamic methods in the curricula of physics and chemistry, as well as among emerging research teams.
© The Author(s) 2026
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