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We report a numerical calculation of the total number of disordered jammedconfigurations $\Omega$ of $N$ repulsive, three-dimensional spheres in a fixedvolume $V$. To make these calculations tractable, we increase the computationalefficiency of the approach of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011))and Asenjo et al. (Phys. Rev. Lett. 112, 098002 (2014)) and we extend themethod to allow computation of the configurational entropy as a function ofpressure. The approach that we use computes the configurational entropy bysampling the absolute volume of basins of attraction of the stable packings inthe potential energy landscape. We find a surprisingly strong correlationbetween the pressure of a configuration and the volume of its basin ofattraction in the potential energy landscape. This relation is well describedby a power law. Our methodology to compute the number of minima in thepotential energy landscape should be applicable to a wide range of otherenumeration problems in statistical physics, string theory, cosmology andmachine learning, that aim to find the distribution of the extrema of a scalarcost function that depends on many degrees of freedom.

Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings