4361

4109

كارشناسي ارشد

فيزيك

اصفهان:دانشگاه صنعتي اصفهان،دانشكده فيزيك

1387

[نه]، 99، [II] ص: -

ص. ع به: فارسي و انگليسي

بهروز ميرزا

محمد حسن علامت ساز

26/12/87

فيزيك

ID4109

به فارسي و انگلسي: قابل رويت در نسخه ديجيتال

The nonlinear Fokker Planck equations related to generalized entropiesAbstractBoltzmann Gibbs statistical mechanics is based on the entropy SBG It enables a successful thermalapproach of some systems such as those involving short range interactions and markovian processes But for systems whose microscopic dynamics is more complex the consept of entropy need to begeneralized In this thesis we brie y review the de nition consequences and applications of Tsallisentropy which generalized the usual Boltzmann Gibbs entropy Boltzmann Gibbs entropy is ap plicable whenever ergodicity is satis ed at microscopic dynamical level Tsallis entropy is based onthe notion of q exponential and presents a nice and practical generalization of Boltzmann Gibbsentropy The termodynamics proposed in this way is generically nonextensive in a sense that willbe quali ed The nonextensive satistical mechanics formalism has emerged naturally as a strongcandidate for dealing appropriately with many real systems that are not satisfactorily describedwithin standard extensive statistical mechanics In this work a class of generalized Fokker Planckequations are reviewed These equations explain time dependence of probability distribution func tion Many important equations and properties of standard statistical mechanics have been extendedwithin the formalism of nonextensive statistical mechanics One of them is H theorem We also re view the H theorem for systems that follow those classes of nonlinear Fokker Planck equations Forthat usually a relation involving terms of Fokker Planck equations and generalized entropic forms isassumed At equilibrium this relation is equivalent to the maximum entropy principle This meansthat Fokker Planck equations conserve energy and mass and increase a generalized entropy func tional until amaximum entropy state is reached According to this relation one may have classes ofnonlinear Fokker Planck equations associate with a single entropic form Nonlinear Fokker Planckequation associated with the Tsallis entropy is a special case of these equations These equations areapplicable in di erent domains of physics We investigate the stationary solutions of those Fokker Planck equations which are related to entropies de ned as arbitrary function of Tsallis entropy Also the transient solutions of equations are determined for linear drifts Transient solutions ofthese equations describe some physical systems far from equilibrium key words Nonextensive statistical mechanics Tsallis entropy Reniy entropy generalized en tropies H Theorem nonlinear Fokker Planck equation stationary solution transient solution

بهروز ميرزا

محمد حسن علامت ساز