Turning intractable counting into sampling: Computing the configurational entropy of threedimensional jammed packings
Abstract
We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, threedimensional spheres in a fixed volume V . To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys. Rev. Lett. 106, 245502 (2011), 10.1103/PhysRevLett.106.245502] and Asenjo et al. [Phys. Rev. Lett. 112, 098002 (2014), 10.1103/PhysRevLett.112.098002] and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology, and machine learning that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.
 Publication:

Physical Review E
 Pub Date:
 January 2016
 DOI:
 10.1103/PhysRevE.93.012906
 arXiv:
 arXiv:1509.03964
 Bibcode:
 2016PhRvE..93a2906M
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Soft Condensed Matter;
 Physics  Computational Physics
 EPrint:
 18 pages, 7 figures