A granular system compresses into a mechanically stable configuration at a nonzero pres- sure in response to the application of an external strain [1–3]. This process is typically referred to as the jamming transition and occurs at a critical volume fraction φ$_{c}$ [3]. The ap- plication of a subsequent external pressure with the concomitant particle rearrangements and compression results in a set of configurations characterized by the system volume V = NV$_{g}$/φ ( φ is the volume fraction of N particles of volume V$_{g}$ ) and applied external stress or pressure p (for simplicity we assume isotropic states). It has been long argued whether the jamming transition is a first-order transition at the discontinuity in the average coordination number, 〈 Z 〉 , or a second-order transition with the power-law scaling of the system’s pressure as the system approaches jamming with φ − φ$_{c}$ → 0 + [4–7]. Previous work [8–10] has proposed to explain the jamming transition by a field theory in the pressure ensemble. Here, we use the idea of “thermalization” of an ensemble of mechanically stable granular materials at a given volume and pressure to study the jamming transition from a thermodynamic viewpoint. For a fixed number of grains, there exist many jammed states [11] confined by the ex- ternal pressure p in a volume V . In an effort to describe the nature of this nonequilibrium system from a statistical mechanics perspective, a pressure-volume ensemble [8, 12–15] was introduced for jammed matter. In the canonical the probability of a state is given by exp[ −W ( ∂S/∂V ) − Γ( ∂S/∂ Γ)], where S is the entropy of the system, W is the volume function measuring the volume of the system as a function of the particle coordinates and Γ ≡ pV is the boundary stress (or internal virial) [9] of the system. Just as ∂E/∂S = T is the temperature in equilibrium system, the temperature-like variables in jammed systems are the compactivity X = ∂V /∂S [12] and the angoricity A = ∂ Γ /∂S [13]. In a recent paper [16] the compactivity was used to describe frictional hard spheres in the volume ensemble. Here, we test the validity of the statistical approach in the combined pressure-volume ensemble to describe deformable, frictionless particles, such as emulsion systems jammed under osmotic pressure near the jamming transition [17]. We demonstrate that the jamming transition can be probed thermodynamically by the angoricity A and the compactivity X . The calculation of jamming “heat” capacities characterizes the sys- tem fluctuations and shows the lack of critical fluctuations in the static quantities as the jamming transition point is approached from above φ → φ + c . Thus, the thermodynami- cal viewpoint determines the order of the phase transition and allows one to calculate the physical observables near jamming. 2