Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds

2015 ◽  
Vol 528 (5) ◽  
pp. 381-393 ◽  
Author(s):  
Fabio Manca ◽  
Pierre-Michel Déjardin ◽  
Stefano Giordano
Keyword(s):  
Brownian Motion ◽  
Statistical Mechanics ◽  
Smooth Manifolds ◽  
Holonomic Systems

Brownian Motion

2018 ◽  
pp. 1-24
Author(s):  
Giovanni Zocchi
Keyword(s):  
Brownian Motion ◽  
Statistical Mechanics ◽  
Concentration Gradient ◽  
Nonequilibrium Statistical Mechanics ◽  
Thermal Fluctuations ◽  
Nonequilibrium System ◽  
Individual Particle ◽  
Equilibrium Concept ◽  
Self Diffusion ◽  
Main Ideas

This chapter provides an introduction to the main ideas of Brownian motion. Brownian motion connects equilibrium and nonequilibrium statistical mechanics. It connects diffusion—a nonequilibrium phenomenon—with thermal fluctuations—an equilibrium concept. More precisely, diffusion with a net flow of particles, driven by a concentration gradient, pertains to a nonequilibrium system, since there is a net current. Without a concentration gradient, the system is macroscopically in equilibrium, but each individual particle undergoes self-diffusion just the same. In this sense, Brownian motion is at the border of equilibrium and nonequilibrium statistical mechanics.

The Reality of Atoms

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Nineteenth Century ◽  
Brownian Motion ◽  
Statistical Mechanics ◽  
Atomic Structure ◽  
Periodic Table ◽  
Albert Einstein ◽  
Ancient Greek ◽  
Structure Of Molecules ◽  
Greek Philosopher ◽  
Jean Perrin

Chapter 3 focuses on the concept of atoms, which dates back to the ancient Greek philosopher Leucippus, who claimed that everything consisted of them. This view began to be accepted among scientists when John Dalton championed it in the 1800s, although he was wrong in his atomic structure of molecules. That was corrected not long after by Jöns Berzelius. From then on the reality of atoms, and whether those of chemistry were the same as those of physics was a matter of debate. The theory of statistical mechanics, developed in the second half of the nineteenth century, helped establish their reality for most physicists, while many chemists were won over later, in part by the periodic table developed by the Russian Dimitri Mendeleev. Nearly every scientist was finally convinced by the explanation of Brownian motion by Albert Einstein and Marian Smoluchowski, whose formulas were verified by Jean Perrin in 1909.

Boltzmann, Ludwig Eduard (1844–1906)

2018 ◽  
Author(s):  
John Blackmore
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Statistical Mechanics ◽  
Central Aspect ◽  
Molecular Movement ◽  
As If

Boltzmann is famous in both physics and philosophy for interpreting thermodynamics in terms of molecular movement as if the second or ‘entropy’ law were merely statistically valid. This approach became a central aspect of statistical mechanics and helped influence Planck’s development of quantum mechanics and Einstein’s work on Brownian motion. The result helped place the reality of atoms, which had long been favoured by most scientists but opposed by many philosophers, beyond reasonable challenge. Toward the end of Boltzmann’s long struggle against the technical objections of physicists and mathematicians and the epistemological criticisms of philosophers the understanding of atoms by those scientists who accepted their reality began changing from indivisible particles to divisible ‘corpuscles’, which included electrons.

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