Entropy: Microstates and Macrostates

Description

Particles in a box start all on one side (ordered, low entropy). They spread randomly to fill the box. A microstate counter shows how many microstates correspond to each macrostate. The Boltzmann entropy formula S = k_B ln Ω is displayed.

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Phases

#	Phase Name	Duration	Description
1	Ordered State	2s	All particles on left side, Ω = 1
2	Spreading	4s	Particles diffuse to fill box
3	Equilibrium	2s	Particles evenly distributed, Ω = max
4	Microstate Counter	2s	Show Ω values for ordered vs disordered
5	Formula	2s	S = k_B ln Ω displayed

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Layout

+--------------------------------------------------+
|  Entropy: Microstates & Macrostates              |
|                                                  |
|  [Box: ●●●●|    ]  Ω = 1    S = low             |
|           ↓ time                                 |
|  [Box: ●● | ●● ]  Ω = 6    S = medium           |
|           ↓ time                                 |
|  [Box: ●●●●    ]  Ω = max   S = high            |
|  (spread out)                                    |
|                                                  |
|  S = k_B ln Ω                                   |
+--------------------------------------------------+

Area Descriptions

• Center: particle box animation
• Right: Ω counter and entropy bar
• Bottom: Boltzmann formula

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Assets & Dependencies

• Fonts: LaTeX / sans-serif
• Manim version: ManimCE 0.19.1

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Notes

• University level
• N = 8 particles for clarity
• Use random walk / diffusion for particle motion
• Entropy bar increases as particles spread