Related papers: Statistical mechanics guides the motions of cm sca…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
We continue discussion of hard-ball models of statistical mechanics, by example of random walk of hard ball immersed into equlibrium ideal gas. Our goal is to highlight decisive role of specific phase-space subsets, despite their…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove…
It is shown that statistical mechanics is applicable to quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, etc., where the residual two-body interaction is sufficiently strong. This interaction mixes…
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
Lifting operators play an important role in starting a kinetic Boltzmann model from given macroscopic information. The macroscopic variables need to be mapped to the distribution functions, mesoscopic variables of the Boltzmann model. A…
One of the greatest contributors of the 20th century among all academician in the field of statistical finance, M. F. M. Osborne published in 1956 [6] an essential paper and proposed to treat the question of stock market motion through the…
In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus…
This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses…
Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
The concept of temperature is one of the key ideas in describing the thermodynamical properties of a physical system. In classical statistical mechanics of ideal gases, the notion of temperature can be described in two different ways, the…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{BG}=-k \sum_{i=1}^W p_i \ln p_i$. It enables a successful thermal approach of ubiquitous systems, such as those involving short-range interactions, markovian processes, and,…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…