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A principled basis for nonequilibrium network flows.

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Summary
This summary is machine-generated.

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.

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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.