Thermodynamics is generally not applicable to systems with energy input and dissipation present, and identifying relevant tools for understanding these far-from-equilibrium systems poses a serious challenge. Excited granular materials have become a canonical system to explore such ideas since they are inherently dissipative due to inter-particle frictional contacts and inelastic collisions. Granular materials also have far reaching practical importance in a number of industries, but accumulated ad-hoc knowledge is often the only design tool.
An important feature of driven granular systems is that the energy input and dissipation mechanisms can be balanced such that a Non-Equilibrium Steady-State (NESS) is achieved. This NESS shares many properties of systems in thermodynamic equilibrium. In particular, the structure and dynamics of the NESS are almost identical to equilibrium systems. Further, we present strong experimental evidence for a NESS first-order phase transition in a vibrated two-dimensional granular fluid. The phase transition between a gas and a crystal is characterized by a discontinuous change in both density and temperature and exhibits rate dependent hysteresis. Finally, we measure a "free energy"-like function for the system, whose minimum determines the state of the system.