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Fluctuation Relations Associated to an Arbitrary Bijection in Path Space
Raphaël Chétrite1, Stefano Marcantoni2,3
1Institut de Physique de Nice (INPHYNI), Université Côte d'Azur, CNRS, 17 rue Julien Lauprêtre, 06200 Nice, France.
Mathematical Physics, Analysis, and Geometry
|October 24, 2025
Summary
We present a framework to discover Fluctuation Relations for vector-valued observables in stochastic systems. This method identifies new relations by analyzing invertible trajectory transformations, generalizing existing theories.
Area of Science:
- Physics
- Statistical Mechanics
- Dynamical Systems
Background:
- Stochastic dynamics govern many physical systems.
- Fluctuation relations offer insights into non-equilibrium thermodynamics.
- Existing relations often focus on specific symmetries.
Purpose of the Study:
- To introduce a general framework for identifying Fluctuation Relations.
- To extend Fluctuation Relations to vector-valued observables.
- To uncover new types of Fluctuation Relations.
Main Methods:
- Developing a framework based on entropic functionals.
- Analyzing invertible, non-involutional transformations in trajectory space.
- Applying the framework to canonical path probability and diffusion processes.
Main Results:
- Identification of a general class of Fluctuation Relations.
- Recovery of known isometric and spatial fluctuation relations as special cases.
- Development of a method for discovering novel Fluctuation Relations.
Conclusions:
- The proposed framework provides a unified approach to Fluctuation Relations.
- New Fluctuation Relations can be systematically derived.
- The findings are applicable to various stochastic processes over finite and asymptotic times.
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