Thermodynamical Analysis Of Self-organized Critical Phenomena

Phase transitions and critical phenomena are the extremely important research fields, such as the transition between ferromagnet and paramagnet, conductor and super-conductor, normal-liquid and super-liquid, etc, which are all belong to critical phenomena. This article educes the non-equilibrium phase transition based on equilibrium phase transition and introduces the general methods for dealing with phase transitions and critical phenomena. Then we emphasize particularly on the behavior of a sort of nonequilibrium system at the critical point –self-organized phenomena, and its origin, development and actuality. Then we combine with example—BTW model to simulate and analyze its characteristic at critical point.First, we research the self-organized critical phenomena and its proper power law character of one-dim sandpile and two-dim sandpile.Then, we analyze the avalanche of the sandpile by rescaled range analysis which was brought forward by H.E.Hurst and find the former avalanche and the latter avalanche have definite relation, ie the system has the long term memory effect. By simulation, we find that when the system evolves to the critical state, large scale avalanche will happen, then the associated length is infinity, and local tiny disturbance will affect the whole system which will introduce the event of avalanche.Furthermore, phase space reconstruction is used to analyze the time sequence of avalanche scale, we find when we choose an appropriate delayed time, and the dimensionality of phase space reconstruction achieves 5, the associated dimensionality doesn't increase any more. The fixed value is 0.0043. To expand a sandpile system to a higher space will help us to exhume some unknown factors , and promote the further develop of search.Lastly, we analyze the system emphasized on the thermodynamics, and look on the BTW sandpile model as a geometrical thermodynamic system, and deduce the variety of energy, entropy , free-energy and their relation of the system in the course of the formation, evolvement up to avalanche of the sandpile. The research indicate that during the formation of the sandpile, the energy of the entropy is increased as a whole, when the system reaches the critical point and the avalanche occurres, energy and entropy are decreased , while entropy density is increased remarkably. Here we adopt configuration entropy and geometrical thermodynamics to deal with the self-organized phenomena, which not only develop the critical theory but have a far-reaching meaning for the research of complex phenomena.