  This paper illustrates how the tools of equilibrium statistical mechanics can
help to explain a far-from-equilibrium problem: the jamming transition in
frictionless granular materials. Edwards ideas consist of proposing a
statistical ensemble of volume and stress fluctuations through the
thermodynamic notion of entropy, compactivity, X, and angoricity, A (two
temperature-like variables). We find that Edwards thermodynamics is able to
describe the jamming transition (J-point). Using the ensemble formalism we
elucidate the following: (i)We test the combined volume-stress ensemble by
comparing the statistical properties of jammed configurations obtained by
dynamics with those averaged over the ensemble of minima in the potential
energy landscape as a test of ergodicity. Agreement between both methods
supports the idea of "thermalization" at a given angoricity and compactivity.
(ii) A microcanonical ensemble analysis supports the idea of maximum entropy
principle for grains. (iii) The intensive variables describe the approach to
jamming through a series of scaling relations as A {\to} 0+ and X {\to} 0-. Due
to the force-volume coupling, the jamming transition can be probed
thermodynamically by a "jamming temperature" TJ comprised of contributions from
A and X. (iv) The thermodynamic framework reveals the order of the jamming
phase transition by showing the absence of critical fluctuations at jamming in
observables like pressure and volume. (v) Finally, we elaborate on a comparison
with relevant studies showing a breakdown of equiprobability of microstates.
