Related papers: Robert W. Zwanzig: Formulated nonequilibrium stati…
The paper is dedicated to the memory of prominent theoretical physicist and mathematician Dr. Vadim Kuznetsov who worked, in particular, in the fields of the nonlinear dynamics, separation of variables, integrability theory, special…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
There is described a spacetime formulation of both nonrelativistic and relativistic elasticity. Specific attention is devoted to the causal structure of the theories and the availability of local existence theorems for the initial-value…
In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
Aspects of the modern dynamical systems approach to thermodynamics of stationary states out of equilibrium with attention to the original conceptions which arose at the beginnings of Statistical Mechanics
In many time-dependent problems of practical interest the parameters and/or initial conditions entering the equations describing the evolution of the various quantities exhibit uncertainty. One way to address the problem of how this…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
Some 80-90 years ago, George A. Linhart, unlike A. Einstein, P. Debye, M. Planck and W. Nernst, has managed to derive a very simple, but ultimately general mathematical formula for heat capacity vs. temperature from the fundamental…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…
This note presents a new definition of nonlinear statistics mean and variance to simplify the nonlinear statistics computations. These concepts aim to provide a theoretical explanation of a novel nonlinear weighted residual methodology…
Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon's interests. In particular, we focus on rigorous non-perturbative results…
This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
We describe a particular approach for the construction of a nonequilibrium statistical ensemble formalism for the treatment of dissipative many-body systems. This is the so-called Nonequilibrium Statistical Operator Method, based on the…
This paper explores special conditions on the starting value of a Collatz sequence which imply that the Collatz conjecture is true. This is the result of the collaboration of a retired mathematics professor (Koelzer) and a retired physics…
This is an intrusion in the life and the mathematics of Norbert A'Campo, intended to be a tribute to him and an acknowledgement of his impact on those who know him and his work. The final version of this paper appears in the book ``Essays…
Translation of Ludwig Boltzmann's paper "\"Uber die Eigenschaften monozyklischer und anderer damit verwandter Systeme" Crelles Journal 98. S. 68-94. 1884 u. 1885 from German into English. In this foundational paper Boltzmann introduced two…