We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Si...

2014 In this paper, we propose a kinetic theory of finite systems, and a new equation for their « microscopic » average behaviour. The equations of particle motion are supposed to be integrable in the mean collective field or/and in an outside given field. The collision time is assumed to be longer than the characteristic orbital time which rules out a local theory of the Fokker-Planck, or Bale...

Recently we introduced a nonlinear partial differential equation (nPDE) of the third order for the first time. This new model equation allows the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly. This also leads to a new formulation in the meaning of the nonlinear Poisson-Boltzmann Equation (nPBE) and therefore we call it the modified PoissonBoltzmann Equation (...

The dielectric with index of refraction n is inserted in the Planck blackbody. The spectral formula for photons in such dielectric medium and the equation for the temperature of photons is derived. The new equation is solved for the constant index of refraction. The photon flow initiates the osmotic pressure of he Debye phonons. The dielectric crystal surface works as the osmotic membrane with ...

A simple analytical approach to estimate thermodynamic properties of model Yukawa systems is presented. The approach extends the traditional Debye-Hückel theory into the regime of moderate coupling and is able to qualitatively reproduce thermodynamics of Yukawa systems up to the fluidsolid phase transition. The simplistic equation of state (pressure equation) is derived and applied to the hydro...

We present several aspects of the screening of charged macromolecules in an electrolyte. After a review of the basic mean field approach, based on the linear Debye-Hückel theory, we consider the case of highly charged macromolecules, where the linear approximation breaks down and the system is described by the full nonlinear Poisson-Boltzmann equation. Some analytical results for this nonlinear...

A model is developed which explains the collective plasma phenomena associated with the extended Franck-Hertz experiment described in an earlier paper by Nicoletopoulos [Eur. J. Phys. 23, 533 (2002)]. The particular focus is on the formation of the free steady-state monotonic double layer. The approach used is a Bernstein-Greene-Kruskal theory in which one postulates the space potential and a s...

According to thermodynamic principle, the critical relative humidity of electrolytes is closely related to their solubility. The authors explored the relationship theoretically and calculated the critical relative humidity of 21 electrolytes in the light of Raoult's law, modified Debye-Hückel model and extended non-random two liquid (NRTL) model from their solubility. The results indicate that ...

We study non-equilibrium behaviors of a particle subjected to high-frequency cutoff noise in terms generalized Langevin equation, where the spectrum internal is considered be Debye form. A closed solution impossible even if equation linear, because Laplace transform memory kernel multi-value function. use numerical method calculate velocity correlation function force-free and probability passin...