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Tatekawa, Takayuki; Sakagami, Masaaki*; Taruya, Atsushi*; Okamura, Takashi*; Ruffo, S.*
no journal, ,
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.
Tatekawa, Takayuki; Sakagami, Masaaki*; Taruya, Atsushi*; Okamura, Takashi*; Ruffo, S.*
no journal, ,
We will discuss relaxation processes toward thermal equilibrium in the long-range interacting system by N-body simulations. In the early stage of its evolution, the system visits quasi-equilibrium state where the value of physical quantities such as mean kinetic energy are different from equilibrium ones. Then it gradually evolves toward thermal equilibrium. We find that this transient states can be described by the polytrope which is given by the one-particle distribution of the energy 
, 
, only when the system has the negative specific heat. The relaxation processes are characterized by increase of index n to infinity which corresponds the Boltzmann distribution. For dynamical evolution, we are trying to accelerate N-body simulations with General-Purpose computation on Graphics Processing Units (GPGPU). GPGPU can accelerate the computation of 2-body interactions.