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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Communication: Maximum caliber is a general variational principle for nonequilibrium statistical mechanics.

Michael J Hazoglou¹, Valentin Walther¹, Purushottam D Dixit²

¹Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA.

The Journal of Chemical Physics

|August 10, 2015

Summary

Maximum Caliber (Max Cal) offers a general variational principle for non-equilibrium statistical mechanics. This principle predicts dynamical distribution functions and extends traditional results far from equilibrium.

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Area of Science:

Statistical Mechanics
Non-Equilibrium Thermodynamics
Theoretical Physics

Background:

Traditional non-equilibrium statistical mechanics often relies on concepts like local equilibrium and entropy dissipation.
A general variational principle applicable beyond near-equilibrium conditions is of significant interest.

Purpose of the Study:

To establish Maximum Caliber (Max Cal) as a general variational principle for non-equilibrium statistical mechanics.
To demonstrate Max Cal's ability to predict dynamical distribution functions and generalize existing theories.

Main Methods:

Formulating Maximum Caliber (Max Cal) as a path entropy maximization under dynamical constraints (e.g., average fluxes).
Applying Max Cal to derive near-equilibrium results and develop generalized relations.

Main Results:

Max Cal successfully reproduces standard near-equilibrium results, including Green-Kubo relations and Onsager's reciprocal relations.
Generalized versions of Onsager and Prigogine results are derived, applicable arbitrarily far from equilibrium.
Max Cal demonstrates broader applicability than traditional methods, not requiring local equilibrium or temperature.

Conclusions:

Maximum Caliber (Max Cal) serves as a powerful and general variational principle for non-equilibrium statistical mechanics.
The principle offers a unified framework for understanding diverse phenomena, including network flows and traffic dynamics.