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Related Experiment Video

Updated: Jul 18, 2026

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

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

Published on: December 4, 2017

Statistical mechanical theory for steady state systems. VI. Variational principles.

¹School of Chemistry F11, University of Sydney, New South Wales 2006, Australia. attard@chem.usyd.edu.au

The Journal of Chemical Physics

|December 15, 2006

Summary

This study evaluates variational principles for nonequilibrium systems. Attard's maximum second entropy principle is identified as the only accurate theory, outperforming others in computer simulations.

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Last Updated: Jul 18, 2026

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

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

Published on: December 4, 2017

Area of Science:

Thermodynamics
Statistical Mechanics
Physical Chemistry

Background:

Several variational principles exist for nonequilibrium systems, including minimum entropy production, maximum entropy production, and minimum dissipation.
These principles offer different theoretical frameworks for understanding irreversible processes.

Purpose of the Study:

To analyze and compare various proposed variational principles for nonequilibrium systems.
To determine the most accurate and viable theoretical approach for describing these systems.

Main Methods:

Analysis of established variational principles: Prigogine's minimum rate of entropy production, maximum rate of entropy production, Onsager's and Onsager-Machlup's minimum dissipation, and Attard's maximum second entropy.
Numerical comparison of theoretical predictions with computer simulation results.

Main Results:

The principles of Onsager and Attard are identified as the only viable theories among those analyzed.
Attard's maximum second entropy principle demonstrated superior accuracy when compared against computer simulation data.
The study discusses the implications of these findings for stochastic differential equations, such as the Langevin equation.

Conclusions:

Attard's maximum second entropy principle is the only accurate variational theory for nonequilibrium systems.
The physical interpretations and mathematical approximations of Onsager's and Attard's theories, while related, differ significantly.
The validated accuracy of Attard's principle has implications for modeling and understanding complex nonequilibrium phenomena.