Four Basic Problems In Nonextensive Statistical Physics And The Thermodynamic Properties Of Generalized Quantum Gases

Nonextensive statistical physics is the extension and deploitation of the conventional (extensive) statistical physics. It's a new theory to deal with some complex systems which present long-range interactions and/or long-duration memory. It can explain some abnormal experimental phenomena that cannot be explained by the theory of the extensive statistical physics. It is a hot problem in the basic physical research fields at present international circumstance. Since there are various different methods in dealing with some complex systems, the nonextensive statistical physics has developed several branches such as Tsallis'statistics, incomplete statistics, q-deformed statistics, etc. Four basic problems in nonextensive statistical physics and the thermodynamic properties of generalized quantum gases are investigated in this dissertation. The main contents are organized as follows.The background and history of the naissance of the nonextensive statistical physics are simply introduced in chapter 1. A research work on self-gravitating systems is cited to analyze the criteria of the so-called"long-range interactions", and consequently, it is expounded that nonextensive statistical physics is good at dealing with such systems. Then, an abnormal phenomenon of 2D turbulence in pure electron plasma is introduced to illuminate that nonextensive statistical physics is the most suitable theory for complex systems which present long-range interactions and/or long-duration memory.The mathematical conformation of Tsallis'entropy and some inherent properties of nonextensive Tsallis'statistics is briefly introduced in chapter 2. On the basis of Tsallis'entropy and the joint probability factorization condition, two controversial problems existing in Tsallis'statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained by strictly mathematical derivation show clearly that like entropy, energy is also nonextensive in Tsallis'statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis'statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers...