Fig. 3: Relationships between dynamical and thermodynamical variables.
From: Testing Adam-Gibbs relationship in tapped granular packings
a Relaxation time \(\tau\) versus \(\chi\) for BUMP (blue Deltas), 3DP (green diamonds), ABS2 (yellow squares), and ABS1 (red circles) systems. The solid curve is a fit of the VFT form: \(\tau ={\tau }_{0}\exp \left[D{\chi }_{0}/\left(\chi -{\chi }_{0}\right)\right]\). Inset: \(\tau\) as a function of \(\phi\). b Rescaled configurational entropy \(\widetilde{S}\) versus rescaled packing fraction \(\widetilde{\phi }\). c Relaxation time \(\tau\) versus \(1/\chi {S}_{c}\) for the four systems. d Relaxation time \(\tau\) versus \(1/\chi \widetilde{S}\). The solid curve is a fit of the Adam-Gibbs relationship: \(\tau \sim \exp [A/\chi \widetilde{S}]\), where \(A\) is a constant. VFT Vogel–Fulcher–Tammann.
