arXiv subjects

Ran Guo

Publications and source records attributed to Ran Guo.

24 records · Page 2Linked to original sources

arXiv2015

The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion

We study the time behavior of the Fokker-Planck equation in Zwanzig rule (the backward-Ito rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation-dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker-Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.

cond-mat.stat-mech↗

arXiv2014

The adiabatic static linear response function in nonextensive statistical mechanics

We analyze the difference between the three generations of the energy constraint in nonextensive statistical mechanics. Using the third generation of the energy constraint, we revise the isothermal static linear response function and then derive the adiabatic static linear response function under the adiabatic condition. We present the relationship between the isothermal and adiabatic linear response functions.

cond-mat.stat-mech↗

arXiv2014

The rate coefficients of unimolecular reactions in the systems with power-law distributions

The rate coefficient formulae of unimolecular reactions are generalized to the systems with the power-law distributions based on nonextensive statistics, and the power-law rate coefficients are derived in the high and low pressure limits, respectively. The numerical analyses are made of the rate coefficients as functions of the nu-parameter, the threshold energy, the temperature and the number of degrees of freedom. We show that the new rate coefficients depend strongly on the nu-parameter different from one (thus from a Boltzmann-Gibbs distribution). Two unimolecular reactions are taken as application examples to calculate their power-law rate coefficients, which obtained with the nu-parameters slightly different from one can be exactly in agreement with all the experimental studies on these two reactions in the given temperature ranges.

physics.chem-ph↗

arXiv2014

Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?

We examine whether the principle of detailed balance holds for the power-law distributions generated from the general Langevin equation under the generalized fluctuation-dissipation relation (FDR). With the detailed balance and the generalized FDR, we derive analytically the stationary power-law distribution from the Ito's, Stratonovich's and Zwanzig's Fokker-Planck equations, and conclude that the power-law distributions can either be a stationary nonequilibrium distribution or an equilibrium distribution, which depend on information about the form of the diffusion coefficient function, and the existence and uniqueness of an equilibrium state.

cond-mat.stat-mech↗

arXiv2012

Power-law behaviors from the two-variable Langevin equation: Ito's and Stratonovich's Fokker-Planck equations

We study power-law behaviors produced from the stochastically dynamical system governed by the well-known two-variable Langevin equations. The stationary solutions of the corresponding Ito's, Stratonovich's and the Zwanzig's (the backward Ito's) Fokker-Planck equations are solved under a new fluctuation-dissipation relation, which are presented in a unified form of the power-law distributions with a power index containing two parameter kappa and sigma, where kappa measures a distance away from the thermal equilibrium and sigma distinguishes the above three forms of the Fokker-Planck equations. The numerical calculations show that the Ito's, the Stratonovich's and the Zwanzig's form of the power-law distributions are all exactly the stationary solutions based on the two-variable Langevin equations.

cond-mat.stat-mech↗

arXiv2012

Energy distribution and energy fluctuation in Tsallis statistics

The energy distribution and the energy fluctuation in the Tsallis canonical ensemble are studied with the OLM formalism but following a new way. The resulting formula for the energy fluctuation is not the same as that in previous work [Liu L.Y. and Du J.L., Physica A 387(2008)5417]. In discussing the application of an ideal gas, we find that the energy fluctuation can not be negligible in the thermodynamic limit, showing the ensemble nonequivalence for this case in Tsallis statistics. We investigate the energy fluctuation with a Tsallis generalized canonical distribution studied by Plastino and Plastino [Phys. Lett. A 193(1994)140] for describing a system in contact with a finite heath bath. For this situation, the two formulae for the energy fluctuation are shown to be equivalent, while the nonextensive parameter q plays a very important role.

cond-mat.stat-mech↗