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This study links macroscopic gradient flows to large-deviation principles in Brownian motion systems. It shows how entropies and free energies can be derived from these principles in non-equilibrium situations.

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Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Non-equilibrium Physics

Background:

  • Otto's characterization of diffusion as an entropic gradient flow.
  • Large-deviation principles (LDPs) describing microscopic dynamics, such as Brownian motion.
  • The established connection between equilibrium thermodynamics and microscopic descriptions.

Purpose of the Study:

  • To explore and generalize the connection between entropic gradient flows and LDPs.
  • To demonstrate how thermodynamic quantities like entropy and free energy can emerge from LDPs in non-equilibrium systems.
  • To present an alternative approach to the hydrodynamic limit for understanding macroscopic behavior from microscopic dynamics.

Main Methods:

  • Sketching the connection between Otto's gradient flow and LDPs.
  • Generalizing this connection to a broader class of physical systems.
  • Applying LDPs to derive thermodynamic quantities in non-equilibrium scenarios.

Main Results:

  • Established a formal link between macroscopic gradient flows and microscopic LDPs.
  • Demonstrated the generalization of this link beyond specific diffusion models.
  • Showcased the derivation of entropies and free energies from LDPs in certain non-equilibrium contexts.

Conclusions:

  • The connection between gradient flows and LDPs offers a powerful framework for non-equilibrium statistical mechanics.
  • This approach provides a novel route to understanding thermodynamic properties from microscopic principles.
  • The findings suggest a unified perspective linking macroscopic continuum descriptions with microscopic stochastic processes.