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Numerically discovered inherent states are always protocol dependent in jammed packings
Eddie Bautista1, Eric I Corwin1
1University of Oregon, Department of Physics and Materials Science Institute, Eugene, Oregon 97403, USA.
Physical Review. E
|May 16, 2026
Summary
Finding inherent states in soft sphere packings is challenging. The largest time step (δ_best) for steepest descent dynamics, which finds these states, rapidly decreases with more particles, making reliable identification impossible for larger systems.
Area of Science:
- Physics
- Computational Science
- Materials Science
Background:
- Soft sphere packings exhibit complex energy landscapes with numerous local minima.
- Inherent states represent the local minima configurations flow towards under continuous dynamics.
- Current discrete-time algorithms may not reliably identify these inherent states.
Purpose of the Study:
- To investigate the reliability of finding inherent states in soft sphere packings using steepest descent dynamics.
- To determine the distribution and scaling of the largest time step (δ_best) required to find an inherent state.
- To assess the feasibility of reliably finding inherent states for systems of increasing particle number.
Main Methods:
- Utilized steepest descent dynamics to explore the energy landscape of soft sphere packings.
- Calculated the distribution of the largest time step (δ_best) that successfully identifies the inherent state.
- Analyzed the dependence of δ_best on system size (N), packing dimension (d), and packing fraction (φ).
Main Results:
- The largest time step (δ_best) follows a Weibull distribution.
- δ_best decreases rapidly with increasing system size (N), following a form between exponential and inverse power law.
- This decrease is weakly dependent on packing dimension (d) and packing fraction (φ), attributed to saddle points.
Conclusions:
- The ability to reliably find inherent states diminishes rapidly as system size increases.
- Steepest descent dynamics become practically incapable of reliably finding inherent states for systems with approximately 64 or more particles.
- Saddle points in the energy landscape are a key factor contributing to the difficulty in finding inherent states for larger systems.
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