Related papers: Planck's Legacy to Statistical Mechanics
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
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 amplitudes, Born rule,…
Many statistical issues arise in the analysis of Particle Physics experiments. We give a brief introduction to Particle Physics, before describing the techniques used by Particle Physicists for dealing with statistical problems, and also…
Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman's graduate statistical mechanics course at Berkeley from the 1972-1973 academic year. Part 1 addresses equilibrium statistical mechanics with topics:…
As yet, there is no underlying fundamental theory for the transplanckian regime. There is a need to address the issue of how the observables in our present Universe are affected by processes that may have occurred at superplanckian energies…
The year 2000 marks the centenary of the Planck function for the blackbody spectral distribution. Here are traced the steps, over 100 years, along the path leading to this important formula.
Nearing a century since its inception, quantum mechanics is as lively as ever. Its signature manifestations, such as superposition, wave-particle duality, uncertainty principle, entanglement and nonlocality, were long confronted as weird…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
In 1924, Satyendra Nath Bose's pioneering work laid the foundation for Bose-Einstein statistics, which describes particles with integral spins. His derivation of Planck's law for blackbody radiation bypassed classical assumptions, relying…
Several authors, including the American Statistician (ASA), have noted the challenges facing statisticians when attacking large, complex, unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of…
Here we have discussed on Fermi-Dirac statistics, in particular, on its brief historical progress, derivation, consequences, applications, etc. Importance of Fermi-Dirac statistics has been discussed even in connection with the current…
We review the possibilities and difficulties for statistical physicists if they apply their methods to biology, economics, or sociology.
In 1963-71, a group of people, myself included, formulated and perfected a new approach to physics problems, which eventually came to be known under the names of scaling, universality, and renormalization. This work formed the basis of a…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Socio-economic inequalities are manifested in different aspects of our social life. We discuss various aspects, beginning with the evolutionary and historical origins, and discussing the major issues from the social and economic point of…
Karl Pearson played an enormous role in determining the content and organization of statistical research in his day, through his research, his teaching, his establishment of laboratories, and his initiation of a vast publishing program. His…
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…
I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely…
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…
The primary aim, in teaching physics, is that the student should gain an understanding of the principles of physics and how to apply them to different problems. A secondary aim is to allow the students to appreciate the scientific approach…