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Entropy Applet

 Rules of this entropy game: At start all cells are filled with the same color (green). A random cell is selected: if green: green is replaced by red, if red: red is replaced by green. Continue. When equipartition (32 green cells, 32 red cells) is reached for the first time, the further distribution is evaluated graphically and numerically.

The number N of microstates (n cells, n1 red, n2 green, n= n1+n2) is given by

Example N(2,2): n=4, n1=2, n2=2:

N(64,0) = 1
N(63,1) = 64
N(62,2) = 2101
N(61,3) = 42,836
N(60,4) = 648,780
.
.
N(33,31) = 1,784,054,207,724,775,680 ≈ 1.78 E18
N(33,31) = 1,839,796,536,686,813,696 ≈ 1.84 E18

Computing the entropy S by the formula S = ln N we get:

S(64,0) = 0
S(63,1) ≈ 4.159
.
S(33,31) ≈ 42.025
S(32,32) ≈ 42.056

Equipartion (32,32) is achieved after 84.3 steps on average (standard deviation +/- 31.6):

Equipartion (18,18) is achieved after 43.7 steps on average (standard deviation +/- 18.7):

 Books Küppers, Bernd-Olaf: Die Berechenbarkeit der Welt, Grenzfragen der exakten Wissenschaften. S. Hirzel, Stuttgart 2012. Entropie und Zeitstruktur, S. 200-210 Eigen, Manfred, and Winkler, Ruth: Das Spiel, Naturgesetze steuern den Zufall. Pieper, München 1975. Kapitel 4:Statistische Kugelspiele Web Links

Updated: 2012 Sep 15