Transient states in two-dimensional long-range interacting system

Tatekawa, Takayuki; Sakagami, Masaaki*; Taruya, Atsushi*; Okamura, Takashi*; Ruffo, S.*

It is important to know equilibrium state of systems for analyses of relaxation process. In statistical physics, the equilibrium state corresponds to maximum entropy state. Although methods to derive the distribution function of the maximum entropy state have been studied for a long time, there was a problem with the convergence of the solution. We have developed new method which is considered the convergence of the solution. The function of the equilibrium state is derived by the maximum state of Boltzmann-Gibbs entropy. Recently several entropy models which are expected to describe the relaxation process have been proposed. Because our method can be applied to various models easily, we can inspect the validity of these models. In this study, we analyze 2-D HMF model which is known as simple long-range interacting system. By the comparison between N-body simulations and the function from various models, we have inspected the models to describe the relaxation process of the systems.