December 19, 2011
Published by Bryan at December 19, 2011
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Entropy (Part 6): Randomness and ensembles

httpvh://youtu.be/wFe2zu2116I After rolling 2, 3, 4, 10 and Avogadro’s dice, as seen in the entries below, it becomes clear that the most random states (most number of ways of rolling a number) always dominate while those with fewer arrangements occur less frequently: 1 Entropy: Randomness by rolling two dice 2 […]
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December 12, 2011
Published by Bryan at December 12, 2011
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Entropy (Part 5): Randomness by rolling Avogadro’s dice

With Avogadro's number of dice, you can roll them as much as you want, and the chance that there is an outcome other than the one that corresponds to the position of the spike is so unlikely you can safely ignore them.
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December 5, 2011
Published by Bryan at December 5, 2011
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Entropy (Part 4): Randomness by rolling ten dice

For 10 dice there are over 60 million arrangements and Figure 1 shows the outcomes for 30,000 rolls.
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November 21, 2011
Published by Bryan at November 21, 2011
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Entropy (part 3): Randomness by rolling four dice

The basic idea is that a physical system has many different arrangements (states) of particles which are consistent with some macroscopic quantity, like the temperature. Boltzmann found that out of all possible ways those particles can be arranged, only those that are consistent with the actual temperature need be considered. The chance of any other arrangements is negligible in comparison. Rolling dice illustrates this nicely.
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November 14, 2011
Published by Bryan at November 14, 2011
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Entropy (Part 2): Randomness by rolling three dice

it is suggested the difficulty students have in understanding that entropy is a measure of randomness can be approached by rolling dice. In the first entry two dice were rolled but in that case there are only 36 arrangements and 10 outcomes (rolls from 2 to 12). This does not show that the most random state dominates (i.e. the one with most number of arrangements consistent with a roll of 7) . To show that more dice need be rolled. In this entry three dice are shown to have more randomness in the outcomes (3 to 18).
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November 8, 2011
Published by Bryan at November 8, 2011
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Entropy (Part 1): Randomness by rolling two dice

To understand entropy, I roll dice. I start with two, then move to three, four, ten and then Avogadro’s constant of dice, and roll them randomly.
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