Related papers: Planck's Legacy to Statistical Mechanics
In this paper I will review some basic aspects of the mechanism of stochastic resonance. Stochastic resonance was first introduced as a possible mechanism to explain long term climatic variation. Since then, there have been many…
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
A hundred years ago, the quantum concept provoked a revolution in science and the search of a new conceptual basis for whole physics, as emphasized by Einstein. In this paper, I discuss the essential features of Planck's works in 1900 on…
In this article we formally investigate the impact of twisted space-time on black-body radiation phenomena, i.e. we derive the $\theta$-deformed Planck distribution function as well as we perform its numerical integration to the…
The research on and application of artificial intelligence (AI) has triggered a comprehensive scientific, economic, social and political discussion. Here we argue that statistics, as an interdisciplinary scientific field, plays a…
We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the…
This is a brief account of the legacy of Ken Wilson in statistical physics, high energy physics, computing and education.
In this paper the detailed investigation of one of the most interesting models in the non relativistic quantum mechanics of one massive particle i.e., introduced by G. Poeschl and E. Teller in 1933 is continued; the starting point of…
Quantizing the transfer of energy and momentum between interacting particles, we obtain a quantum impulse equation and relations that the corresponding mechanical power, force and torque satisfy. In addition to the energy-frequency and…
It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is…
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
The aim of this work is to try to bridge over theoretical immunology and disordered statistical mechanics. Our long term hope is to contribute to the development of a quantitative theoretical immunology from which practical applications may…
Hawking radiation and black hole thermodynamics are well understood in the frameworks of quantum field theory and general relativity, with contemporary extensions in string theory, AdS/CFT, and loop quantum gravity. However, an open…
From the "vibrating string" and "Kepler's equation" theories to relativistic quantum fields, perturbation theory, (divergent) series resummations, KAM theory.
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical…
We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…