A subdynamic based kinetic equation (SKE) for quantum information density (QID) is presented and using this is shown that the Liouville equation, Master equation and Fokker–Planck equation for QID all share the same formalism as the density operator. This allows one to directly use QID for...

Recent research has established log-periodic power law (LPPL) patterns prior to the detonation of the German stock index (DAX) bubble in 1998. The purpose of this article is to explore whether a Langevin equation extracted from real world data can generate synthetic time series with comparable...

The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and...

In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for phase-space lattice with long-range jumps of power-law types is suggested. We prove that the continuum limit transforms this lattice equation into Liouville equation with conjugate...

The general formulas of the network for the power exponents of the degree distribution and the entropy are presented based on an open Liouville equation for the driven network. The proposed harmonious unifying hybrid preferential models (HUHPM) have been studied using the obtained formalism, in...

A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in Rn, or Sn,n∈N, which are distributed according to the configurational microcanonical measure δ(E−H), or rather some regularization thereof, where H is the...

A variational method for the classical Liouville equation is introduced that facilitates the development of theories for non-equilibrium classical systems. The method is based on the introduction of a complex-valued auxiliary quantity Ψ that is related to the classical position-momentum...

Smoluchowski and Fokker–Planck equations for the stochastic dynamics of order parameters have been derived previously. The question of the validity of the truncated perturbation series and the initial data for which these equations exist remains unexplored. To address these questions, we take...

Travelling wave solutions for the Boussinesq-double sine-Gordon (B-sine-Gordon) equation, the Boussinesq-double sinh-Gordon equation (B-sinh-Gordon), and the Boussinesq-Liouville (BL) equation are formally derived. The approach rests mainly on the variable separated ODE method. Distinct sets of...

We consider the evolution of a system composed of N non-interacting point particles of mass m in a container divided into two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area A of the container, the number N of particles, and...