Related papers: Frechet differentiability of molecular distributio…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
It is shown that the partial temperatures of a homogeneous multicomponent gas mixture in the thermodynamical equilibrium cannot be equal to each other. New general solutions for equilibrium distribution functions of the multicomponent…
We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a \emph{minimal} ratchet model. We extend our previous work on this model, by further investigating the constraints imposed by the Fluctuation…
The partition function, $U$, the number of available states in an atom or molecules, is crucial for understanding the physical state of any astrophysical system in thermodynamic equilibrium. There are surprisingly few {\em useful}…
The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
Many complex ecosystems, such as those formed by multiple microbial taxa, involve intricate interactions amongst various sub-communities. The most basic relationships are frequently modeled as co-occurrence networks in which the nodes…
We developed the functional form of the two-point correlation function under the approximation of fixed particle number density n(bar). We solved the quasi-linear partial differential equation (PDE) through the method of characteristics to…
This work provides calculus for the Fr\'echet and limiting subdifferential of the pointwise supremum given by an arbitrary family of lower semicontinuous functions. We start our study showing fuzzy results about the Fr\'echet…
A flowing pair of particles in inertial microfluidics gives important insights into understanding and controlling the collective dynamics of particles like cells or droplets in microfluidic devices. They are applied in medical cell analysis…
We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition between the quantum and classical statistics of two identical particles is described by the particles having identical multiple…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform…
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…
We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons and identical fermions. By exploiting the fact that different types of particles are associated with…
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…
We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to the thermal equilibrium along the transformation. We derive a general analytic expression for the…
We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain…