Related papers: Statistical Mechanics in a Nutshell
Since the problem: "What is statistics?" is most fundamental in sceince, in order to solve this problem, there is every reason to believe that we have to start from the proposal of a worldview. Recently we proposed measurement theory (i.e.,…
Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization $\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
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…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-\sum_{i}p_i^q}{q-1} (q \in {\cal R}; S_1=-k\sum_{i}p_i \ln p_i)$. Among others, we focus on possible…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
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…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
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…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…