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blog.kiel.how/NS162notes/Lesson 04 - Equilibrium and Coarsegraining.html

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In Lesson 1, we noted that as systems approach equlibrium, the energy and matter in the system tends to “spread out”. In this lesson, we will use coarse-graining as a way to study the approach to an equilibrium state. In this lesson we focus on the spreading out of matter in the billiard balls model; in later lessons we return to study the spreading out of energy. This animation shows a billiard ball model initialized with all of the particles on one half of the box. Intuitively, it’s clear that in equilibrium, the particles are spread out through the whole box. How can we quantify this though? What makes a configuration with the particles spread out over the whole table different from one where they are localized on one half? We can make a clearer definition of equilbrium by defining macroscopic coarse-grained variables. As a simple example, we can choose the number of atoms on the left hand side of the box 𝑁 𝐿 and the number of atoms on the right hand side of the box 𝑁 𝑅 as m

Lesson 4 - Equilibrium and Coarsegraining In Lesson 1, we noted that as systems approach equlibrium, the energy and matter in the system tends to “spread out”. In this lesson, we will use coarse-graining as a way to study the approach to an equilibrium state. In this lesson we focus on the spreading out of matter in the billiard balls model; in later lessons we return to study the spreading out of energy. An Expanding Gas This animation shows a billiard ball model initialized with all of the particles on one half of the box. Expanding Gas Intuitively, it’s clear that in equilibrium, the partic

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