Research On The Thermodynamical Problems Of Self-gravitating Systems On Basis Of Nonextensive Statistical Theory

In the classical gravitational-thermodynamics,due to the concavity breaking of Boltzmann entropy,the negative specific heat always exist in the self-gravitating systems.It is related to the dynamic instability of system,which leads to the gravothermal catastrophe phonemenon.Therefore,the self-gravitating system is always unstable.However,this point is inconsistent with the observations.The realistic gravitational systems always evolve from instable state to stable state.In this doctoral thesis,we researched on these problems in the representation of nonextensive statistical mechanics.We proposed the temperature duality principle,which resolves problem of temperature definition in nonextensive statistics,which troubles people for long time.This principle splits the temperature concept into two parts,called physical temperature and Lagrange temperature respectively,which play different roles in nonextensive statistics.Applying this principle into actual gas,a result corresponding to experiment is obtained.It is also used to prove the equivalence of two power law distribution functions,i.e.,the isothermal distribution and the nonisothermal distribution.We discuss and emphasize the importance of Du's relation,which is special in the nonextensive statistics.It expresses the relation of the Lagrange temperature gradient and the gradient of long range potential.On basis of Du's relation we give two explanations of nonextensive parameter in self-gravitating systems.One of them has become the statistical basis of the gravitational temperature concept defined later.Due to Du's relation,we can give the convective instability criterion expressed by nonextensive parameter.By use of Du's relation,and also the homogeneous condition of nonextensive parameter we define the gravitational temperature.It is related to the Tsallis equilibrium state,and its gradient induces the so-called gravitational heat flux.It can be sued to study the hierarchical structure in the solar interior,among which we find that,there exits gravitational heat flux in different regions inside the sun.We prove the boundedness of nonextensive entropy in self-gravitating systems,which indicates the existence of maximum of such entropy,and the concavity breaking of classical entropy can no longer occur.In light of the concavity of nonextensive entropy we define the gravitational heat capacity.We re-deduce the thermodynamic stability criterion in canonical ensemble,in the representation of nonextensive statistics,and also deduce its parameter expression.We research on the gravothermal catastrophe phenomenon in the framework of nonextensive statistics.By improving the peers' work,we verify that the evolution of gravitational systems result in the increase of nonextensive parameter.And the parameter increase can further produce the decline of polytropic index.As a result the system satisfies the stability criterion eventually,to fly into a stable state;therefore gravothermal catastrophe process is stopped.The above process shows that the parameter plays an important role in the evolution of astrophysical systems.Due to the parameter evolution,an isolated self-gravitating system can evolve into a core-halo structure,while a system in thermal contact with a heat reservoir can not develop out such a structure.And also due to such parameter evolution,the entropy of a given self-gravitating system can decrease with time at equilibrium state.This does not violate the second law of thermodynamics.That is because the parameter evolution at that moment is linked to the release of radiation energy of gravitational system.In such a situation,the system is not isolated any more,but combines the vacuum to become a composite system.It can be easily proved that,the entropy of the composed system increases with the release of radiation energy.