Latent heat at the glass transition in a tapped granular pile*

The compaction of a granular pile subjected to a series of discrete taps has been widely investigated due to its relevance in both, basic and applied science. The well-know Chicago experiment [1] showed that, given a granular pile subjected to taps of controlled intensity, it is possible to define the density of the system as a reversible function of the tap intensity. Using a continuum annealing protocol, where the intensity Γ of the tap was reduced at several distinct, constant variation rates dΓ after each tap, we have shown [2,3] that, although for high tap intensities the density φ of the system can indeed be defined solely by the tap intensity, for low tap intensities φ will become also a function of the protocol followed to reach the given intensity. This behaviour is characteristic of non-equilibrium (“glassy”) systems. The transition between these two regimes is accompanied by a region of high susceptibility, where a peak on the density fluctuations Δφ can be observed while the pile traverses the “glass” transition. In this presentation we will show that this region of high susceptibility is also accompanied by a hysteretic behaviour. We will discuss how the local effective energy of the perturbation [3], measured as the maximum kinetic energy of the grains during the tap as a function of its position on the pile, can be used to define a latent heat, responsible for this hysteretic behaviour.