Memory and Kovacs effects in the parking-lot model: an approximate statistical-mechanical treatment

This chapter deals with the parking-lot model, which provides a qualitative description of the main features of the phenomenology of granular compaction. The term of “glassy-dynamics” is now commonly used to describe out-of-equilibrium systems that display such generic features as very slow kinetics that prevent the system from reaching equilibrium in any reasonable experimental timescale, aging phenomena, and history-dependent processes like hysteresis and memory effects. Among such systems are the “not-too-strongly” vibrated granular materials. In the recent years, there has been a surge of research activity in this field, partly driven by the goal of providing a statistical-mechanical description of these out-of-equilibrium situations. It is derived that approximate kinetic equations for this model, equations that are based on a 2-parameter generalization of the statistical mechanical formalism first proposed by Edwards and coworkers. The chapter highlights that history dependent effects, such as memory and Kovacs effects, are captured by this approach.