Related papers: Statistical Mechanics in Collective Coordinates
Ferromagnetic models are harmonic oscillators in statistical mechanics. Beyond their original scope in tackling phase transition and symmetry breaking in theoretical physics, they are nowadays experiencing a renewal applicative interest as…
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion…
Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…
Engines are open systems that can generate work cyclically, at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…
As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion…
For a phenomenon $\boldsymbol{f}$ that is a function of $n$ factors, defined on a finite abelian group $G$, we derive its population statistics solely from its Fourier transform $\hat{\boldsymbol{f}}$. Our main result is an…
An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the…
We introduce a fundamental theory for the kinetics of systems of classical particles. The theory represents a unification of kinetic theory, Brownian motion and field theory. It is self-consistent and is the dynamic generalization of the…
Special high-accuracy direct force summation N-body algorithms and their relevance for the simulation of the dynamical evolution of star clusters and other gravitating N-body systems in astrophysics are presented, explained and compared…
We study the Brownian motion on the non-compact Grassmann manifold $\frac{\mathbf{U}(n-k,k)} {\mathbf{U}(n-k)\mathbf{U}(k)}$ and some of its functionals. The key point is to realize this Brownian motion as a matrix diffusion process, use…
We present a method how to estimate from experimental data of a turbulent velocity field the drift and the diffusion coefficient of a Fokker-Planck equation. It is shown that solutions of this Fokker-Planck equation reproduce with high…
The focus of our study in this paper is on the active dynamics and a fractional generalized Langevin equation with a memory kernel K(t). The Fokker-Planck equation is obtained by deriving it from a second-order differential equation. The…
We define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
Understanding the statistical behavior of the heat in stochastic systems gives us insight about the thermodynamics of such systems. Using the recently proposed Relativistic Stochastic Thermodynamics, we investigate the statistics of the…
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^\mu introduces a foliation on the…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold…
Statistical mechanical concepts and processes such as decoherence, correlation, and dissipation can prove to be of basic importance to understanding some fundamental issues of quantum cosmology and theoretical physics such as the choice of…
Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her…