Related papers: Planck's Legacy to Statistical Mechanics
Planck's law for black-body radiation marks the origin of quantum theory and is discussed in all introductory (or advanced) courses on this subject. However, the question whether Planck really implied quantisation is debated among…
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
Along the lines of nonextensive statistical mechanics, based on the entropy $S_q = k(1- \sum_i p_i^q)/(q-1) (S_1=-k \sum_i p_i \ln p_i)$, and Beck-Cohen superstatistics, we heuristically generalize Planck's statistical law for the…
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…
Here we present some results that would possibly have attracted the attention of the physics community in the early days of quantum mechanics in such a way that its development could have been different from what we see today. We will first…
In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus…
Planck introduced his famous units of mass, length and time a hundred years ago. The many interesting facets of the Planck mass and length are explored. The Planck mass ubiquitously occurs in astrophysics, cosmology, quantum gravity, string…
Professor Chen Ning Yang has made seminal and influential contributions in many different areas in theoretical physics. This talk focuses on his contributions in statistical mechanics, a field in which Professor Yang has held a continual…
Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and why the material world appears to be as stable as it is…
The interplay between optical and statistical physics is a rich and exciting field of study. Black body radiation was the first application of photon statistics, although it was initially treated as a problem of the cavity oscillators in…
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…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
This paper explores the historical development of the theory of quantum mechanics between 1900 and 1927 by chronological examination of the foundational papers and ideas. Beginning with Planck's introduction of energy quantisation in…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
The application of classical methods of statistical mechanics, originally developed by Ludwig Boltzmann in gas dynamics, to the description of social phenomena is a successful story that we try to outline in this paper. On one hand, it is…
In the introduction to this volume, we discuss some of the highlights of the research career of Chuck Newman. This introduction is divided into two main sections, the first covering Chuck's work in statistical mechanics and the second his…
In this paper I shall try to sketch some typical aspects of Erich Lehmann's contributions to statistics through his research, his teaching, his service to the profession and his personality.
I write about H\'ector, his contributions to the early work in the quark model, and a general discussion of quantum statistics