Study Linear Filament Model Using Nonextensive Statistical Mechanics And Put It Into Use In Phase Transition

This paper discusses the difficulties of traditional statistical mechanics. To address these difficulties, the birth of the nonextensive statistical mechanics and successfully used in the physical properties of complex systems. At present, some methods to research phase transition always take the thermodynamic limit, and the thermodynamic limit is the embodiment of "the extensive property"; Furthermore, the phase transition can occur in any macroscopic scale, not necessarily to take the thermodynamic limit. This article study the linear filament system by the E-V distribution based on Tsallis entropy in the nonextensive statistics, found that with the changes of the nonextensive parameter q, it occur the structural phase transition, while we didn’t take the thermodynamic limit in the reasoning and calculation.Firstly, based on the E-V distribution of deformed incomplete Shannon entropy, we discuss thermodynamic property of a linear filament model that is composed of N units, and every unit may be at m energy states, get its unified formula of partition function, internal energy, average length, entropy and chemical potential. Use the Mathmatica software for numerical calculation, and illustrates the calculation results in figure. It clearly reflects the deviation degree of thermodynamic properties to q=1under different q. When the nonextensive parameter q close to1, the deviations of thermodynamic properties of a linear filament from GBS is not obvious while the absolute temperature T is low. But the deviations are increasing as the increase of absolute temperature T, this deviation degree has nothing to do with unit number N of linear filament.Secondly, based on the E-V distribution of Tsallis entropy, we get its formula of partition function, internal energy, average length, entropy and chemical potential when m=3and m=4. We also make numerical calculation and drawing figure by using the Mathmatica software, illustrates the changing trend of the internal energy, average length, entropy and chemical potential with temperature T in the linear filament. And the results show that:as long as each energy state of linear filament εi (i=a,b,c or d) is sure, we can find fixed critical temperature Tc> and there is a sharp peak in the variation curve of internal energy, average length, entropy and chemical potential at the critical temperature TC, especially within a very steep peak in internal energy and average length. Through the verification of the order parameter scaling law of the phase transition theory, we can obtain that, this phenomenon of occur steep peak at TC is similar to the structural phase transition.