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

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Frequency-dependent fluctuation-dissipation relations in granular gases.

Guy Bunin¹, Yair Shokef, Dov Levine

¹Department of Physics, Technion, Haifa 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 23, 2008

Summary

The Green-Kubo relation is violated in granular gases. For two models, effective temperatures calculated using this relation do not consistently match the granular temperature, indicating a breakdown of the relation.

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Area of Science:

Physics
Statistical Mechanics
Non-equilibrium Thermodynamics

Background:

The Green-Kubo relation connects transport coefficients to equilibrium fluctuations.
Granular gases are systems of macroscopic particles interacting via dissipative collisions.
Understanding the thermodynamic properties of granular gases is crucial for non-equilibrium statistical mechanics.

Purpose of the Study:

To investigate the validity of the Green-Kubo relation in two distinct models of granular gases.
To compare effective temperatures derived from the Green-Kubo relation with the granular temperature.

Main Methods:

Analysis of the Green-Kubo relation for the Maxwell model of granular gases.
Calculation of the Green-Kubo relation in the high-frequency limit for a mean-field granular gas model.
Comparison of effective temperatures with granular temperature across different frequency regimes.

Main Results:

In the Maxwell model, the effective temperature from Green-Kubo is frequency-independent and equals the granular temperature.
For the mean-field model, the high-frequency limit of the effective temperature also matches the granular temperature.
Previous findings show a discrepancy between zero-frequency (Einstein relation) and granular temperatures.

Conclusions:

The Green-Kubo relation is shown to be violated for granular gases.
The effective temperature derived from Green-Kubo relations depends on the frequency and the model.
This violation highlights the challenges in applying equilibrium statistical mechanics concepts to dissipative systems.