Boltzmann Temperature in out-of-equilibrium lattice gas

We investigate the quench of Ising and Potts models via Monte Carlo dynamics, and find that the distribution of the site-site interaction energy has the same form as in the equilibrium case. This form directly derives from the Boltzmann statistics and allows to measure the instantaneous temperature during the systems relaxation. We find that, after an undercritical quench, the system equilibrates in a finite time at the heatbath temperature, while the energy still decreases due to the coarsening process.