Edwards Thermodynamics for a Driven Athermal System with Dry Friction

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Complex systems

Background:

• Understanding the thermodynamics of disordered systems is crucial.
• Friction in spring-block models exhibits complex behaviors.
• Tapping dynamics can alter system configurations and properties.

Purpose of the Study:

• To derive Edwards thermodynamics for a 1D spring-block model with dry friction.
• To analytically explain the observed correlation length divergence.
• To investigate the role of mechanically stable configurations and critical points.

Main Methods:

• Semianalytical transfer operator techniques.
• Analytical characterization using Gaussian approximation.
• Analysis of mechanically stable configurations.

Main Results:

• Successfully obtained Edwards thermodynamics for the model.
• Reproduced the linear divergence of correlation length with energy density.
• Linked the divergence to an infinite temperature critical point.

Conclusions:

• The transfer operator method provides a powerful tool for analyzing such systems.
• The model exhibits critical behavior related to friction and system stability.
• The findings offer insights into the statistical mechanics of disordered materials.