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چكيده انگليسي :

Energy Fluctuations in Tsallis Statistical Mechanics Student name Abbas Helmi Email address a helmi@ch iut ac ir Date of submission 1389 7 14 Department of Chemistry Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Dr Ezat Keshavarzi keshavrz@cc iut ac ir Abstract As we all aware of it there exist plenty of natural phenomenon which their thermodynamic behavior as a result of nonextensivity is not justifiable by common Boltzman Gibbs Statistical Mechanics Therefore in order to justifying these phenomenons expansion of Boltzman Gibbs entropy seems to be essential In this course a novel Statistical Mechanics based on the general definition of entropy was presented by Tsallis In this dissertation the amount of energy fluctuation for two models ideal gas and harmonic oscillator in the second and forth version of Tsallis statistical Mechanics has been considered The results demonstrate that energy fluctuation in the second method of Tsallis Statistical Mechanics is going to be controlled by three terms in which the first term is in relation with heat capacity where in Tsallis and Boltzman Gibbs Statistical Mechanics will be appeared with various coefficients according to the type of Statistical Mechanics and definition of average energy The second and third terms will be under control by three factors incoming nonextensivity to the entropy function weighting of the probability function and unnormalized of the energy constraint Fluctuation analysis in the fourth method of Tsallis Statistical Mechanics seems to be the most perfect method of this Statistical Mechanics shows that the amount of energy fluctuation in the range of qs less than unity is always smaller then Boltzman Gibbs and on the other hand for qs larger than unity is larger than Boltzman Gibbs all the times Indeed when the number of accessible states of system is more than Boltzman Gibbs Statistics relative fluctuation of energy would be further and in contrary when the number of accessible states is fewer than Boltzman Gibbs the fluctuation will be fewer too It is praiseworthy to mention that the amount of energy fluctuation in the second method in the case of harmonic oscillator while would be less than Boltzman Gibbs due to the few number of accessibility states Nevertheless energy fluctuation regarding an ideal gas thanks to abundance of number of accessible states in almost all qs except that q which is a little less than unity is more than Boltzman Gibbs Statistics Generally speaking extensive number of energy fluctuations and consequently fluctuation of quantities is one of the main drawbacks of the second Tsallis Statistical Mechanics Actually in this method we cannot consider the average mechanical property of the system as equal as the thermodynamic property in other words the average of energy lacks physical meaning Keywords Energy fluctuations nonextensive systems Harmonic oscillator Ideal gas

حلمي، عباس

افت و خيز انرژي در مكانيك آماري تساليس

سامانه هاي نافزونور , نوسانگرهماهنگ , گاز ايده آل