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A principled basis for nonequilibrium network flows
Ying-Jen Yang1, Ken A Dill2,3,4
1Laufer Center for Physical and Quantitative Biology, Stony Brook University, New York, NY, USA. ying-jen.yang@stonybrook.edu.
Nature Communications
|April 8, 2026
Summary
Caliber Force Theory generalizes equilibrium statistical physics to nonequilibria using path entropies and dynamic observables. This framework derives generalized relations and constructs dynamical models, resolving paradoxes in stochastic transport.
Area of Science:
- Statistical Physics
- Non-equilibrium Thermodynamics
- Theoretical Physics
Background:
- Equilibrium statistical physics relies on conservation laws, variational principles, and Legendre transforms.
- Key observables (U, V, N) are linked to driving forces (T, p, μ).
- Extending these principles to non-equilibrium systems remains a challenge.
Purpose of the Study:
- To generalize the framework of equilibrium statistical physics to non-equilibrium systems.
- To introduce Caliber Force Theory, utilizing path entropies and dynamic observables.
- To derive generalized conjugate relations and construct dynamical models for complex systems.
Main Methods:
- Replacing state entropies with path entropies.
- Utilizing dynamic observables such as node probabilities, edge traffics, and cycle fluxes.
- Applying Legendre Transforms to dynamic observables to derive generalized forces.
Main Results:
- Derivation of generalized Maxwell-Onsager and fluctuation-response relations applicable far from equilibrium.
- Construction of dynamical models based on mixed force-observable constraints.
- Discovery of relationships including a generalized Einstein relation and an "equal-traffic" rule for molecular motors.
Conclusions:
- Caliber Force Theory provides a unified framework for non-equilibrium statistical physics.
- The theory successfully resolves dynamical paradoxes in stochastic transport.
- It offers new insights into molecular motors and stochastic processes.
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