The Emergence of Statistical Mechanics

2017 ◽  
Author(s):  
Olivier Darrigol ◽  
Jürgen Renn
Keyword(s):  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Statistical Physics ◽  
Second Law Of Thermodynamics ◽  
Boltzmann Distribution ◽  
Probabilistic Interpretation ◽  
Specific Heats ◽  
Mechanical Models ◽  
History Of ◽  
Thermal Phenomena

This article traces the history of statistical mechanics, beginning with a discussion of mechanical models of thermal phenomena. In particular, it considers how several circumstances, including the establishment of thermodynamics in the mid-nineteenth century, led to a focus on the model of heat as a motion of particles. It then describes the concept of heat as fluid and the kinetic theory before turning to gas theory and how it served as a bridge between mechanics and thermodynamics. It also explores gases as particles in motion, the Maxwell–Boltzmann distribution, the problem of specific heats, challenges to the second law of thermodynamics, and the probabilistic interpretation of entropy. Finally, it examines how the results of the kinetic theory assumed a new meaning as cornerstones of a more broadly conceived statistical physics, along with Josiah Willard Gibbs and Albert Einstein’s development of statistical mechanics as a synthetic framework.

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

Supradegeneracy and the Second Law of Thermodynamics

2020 ◽  
Vol 45 (2) ◽  
pp. 121-132
Author(s):  
Daniel P. Sheehan
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Population Inversion ◽  
Laboratory Experiments ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Boltzmann Factor ◽  
Energy Currents ◽  
Non Equilibrium

AbstractCanonical statistical mechanics hinges on two quantities, i. e., state degeneracy and the Boltzmann factor, the latter of which usually dominates thermodynamic behaviors. A recently identified phenomenon (supradegeneracy) reverses this order of dominance and predicts effects for equilibrium that are normally associated with non-equilibrium, including population inversion and steady-state particle and energy currents. This study examines two thermodynamic paradoxes that arise from supradegeneracy and proposes laboratory experiments by which they might be resolved.

scholarly journals Knotting the MECO Network

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 141
Author(s):  
Reinhard Folk
Keyword(s):  
Statistical Physics ◽  
Condensed Matter ◽  
Theoretical Models ◽  
Iron Curtain ◽  
Solid State Physics ◽  
Scientific Exchange ◽  
History Of ◽  
Traditional Fields ◽  
Historical Resources ◽  
Further Development

The Conferences of the Middle European Cooperation in Statistical Physics (MECO) were created as an attempt to establish and maintain an exchange between scientists in the fields of statistical and condensed matter physics from Western and Eastern countries, overcoming the hurdles of the Iron Curtain. Based on personal remembrance and historical resources, the genesis and further development of MECO meetings is described. The annual meetings were interrupted in 1991 by the Yugoslav War but were re-established in 1993 and continue today. Although the fall of the Iron Curtain and the European Research programs changed the situation for the meetings considerably, the ties created by MECO still are useful to help scientific exchange. The history of European (and not only) statistical physics and the history of the MECO are tightly intertwined. It started in a time where an essential breakthrough has been achieved in statistical physics describing the features near phase transitions. In addition to the merging of solid-state physics and field theory concepts, the application of numerical methods (Monte Carlo methods) added a new pillar besides exact solutions and experiments to check theoretical models. In the following, the scientific emphasis (in general) has changed from the traditional fields of the first MECO to complexity and interdisciplinary themes as well.

Statistical Mechanics, Kinetic Theory, and Stochastic Processes

Physics Today ◽  
1973 ◽  
Vol 26 (12) ◽  
pp. 57-59 ◽  
Author(s):  
C. V. Heer ◽  
E. A. Mason
Keyword(s):  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Stochastic Processes

The Royal Society’s first rejection of the kinetic theory of gases (1821), John Herapath versus Humphry Davy

1963 ◽  
Vol 18 (2) ◽  
pp. 161-180 ◽  
Keyword(s):  
Kinetic Theory ◽  
Royal Society ◽  
Kinetic Theory Of Gases ◽  
Early Nineteenth Century ◽  
Important Distinction ◽  
Mathematical Inquiry ◽  
History Of ◽  
Humphry Davy ◽  
Apparent Similarity ◽  
Caloric Theory

On 24 May 1820 a manuscript entitled ‘A Mathematical Inquiry into the Causes, Laws and Principal Phenomena of Heat, Gases, Gravitation, etc.’ was submitted to Davies Gilbert for publication in the Philosophical Transactions of the Royal Society . The author was John Herapath (1790-1868), and his article included a comprehensive (if somewhat faulty) exposition of the kinetic theory of gases. Sir Humphry Davy, who assumed the Presidency of the Royal Society on 30 November 1820, became primarily responsible for the fate of the article and wrote several letters to Herapath concerning it. After it became clear that there was considerable opposition to its publication by the Royal Society, Herapath withdrew the article and sent it instead to the Annals of Philosophy , where it appeared in 1821 (1). Herapath’s theory received little notice from scientists until thirty-five years later, when the kinetic theory was revived by Joule, Krönig, Clausius, and Maxwell. The incident is significant in the history of physical science because it illustrates an important distinction between the two doctrines concerning the nature of heat—the kinetic and the vibration theories—a distinction which is often forgotten because of the apparent similarity of both doctrines as contrasted with the caloric theory. It also throws some light on the character of early nineteenth century British science, both in and out of the Royal Society.

Beyond Chance and Credence

2021 ◽  
Author(s):  
Wayne C. Myrvold
Keyword(s):  
Twentieth Century ◽  
Statistical Mechanics ◽  
Physical World ◽  
Degrees Of Belief ◽  
History Of ◽  
Thermodynamics And Statistical Mechanics

Probability concepts permeate physics. This is obvious in statistical mechanics, in which probabilities appear explicitly. But even in cases when predictions are made with near-certainty, there is are implicit probabilistic assumptions in play, as it is assumed that molecular fluctuations can be neglected. How are we to understand these probabilistic concepts? This book offers a fresh look at these familiar topics, urging readers to see them in a new light. It argues that the traditional choices between probabilities as objective chances or degrees of belief is too limiting, and introduces a new concept, called epistemic chances, that combines physical and epistemic considerations. Thinking of probabilities in this way solves some of the puzzles associated with the use of probability and statistical mechanics. The book includes some history of discussions of probability, from the eighteenth to the twentieth century, and introductions to conceptual issues in thermodynamics and statistical mechanics. It should be of interest to philosophers interested in probability, and to physicists and philosophers of physics interested in understanding how probabilistic concepts apply to the physical world.

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