Measuring the configurational temperature of a binary disc packing

Area of Science:

• Physics
• Statistical Mechanics
• Materials Science

Background:

• Jammed granular packings are athermal, differing from systems typically analyzed by statistical mechanics.
• A statistical mechanics framework for static granular media uses configurational temperature (X) instead of thermodynamic temperature.
• Configurational temperature (X) quantifies the dependence of mechanically stable configurations on volume.

Purpose of the Study:

• To experimentally test the quantitative agreement of four proposed methods for measuring configurational temperature (X).
• To determine if configurational temperature (X) behaves as an intensive variable in experimental granular packings.

Main Methods:

• Utilized experimental binary disc packings to collect data.
• Applied four distinct methods to measure configurational temperature (X) from the experimental dataset.
• Analyzed the Voronoi volume distribution and contact number for X calculations.

Main Results:

• Only two of the four methods for measuring configurational temperature (X) yielded quantitatively consistent results.
• This suggests that at least two of the proposed measurement methods are inaccurate.
• Configurational temperature (X) was found to be an intensive variable only for sample sizes exceeding approximately 200 particles.

Conclusions:

• Significant discrepancies exist among current methods for calculating configurational temperature (X) in granular systems.
• The intensive nature of configurational temperature (X) is size-dependent, influenced by particle volume correlations.
• Findings necessitate a re-evaluation of existing methods and understanding of configurational temperature in granular statistical mechanics.