Posted by on Dec 16, 2011 in Entropy | 2 comments

# Entropy (Part 4): Randomness by rolling ten dice

In order to illustrate the concept of randomness as it pertains to entropy, in a series of entries different numbers of dice have been rolled.

Entropy 1: Randomness by rolling two dice

Entropy 2: Randomness by rolling three dice

Entropy 3: Randomness by rolling four dice

A die with six random states is used to illustrate a particle, so as the number of dice increases, so the number of states increases. For n dice  there are 10n different ways they can be rolled.   The roll that comes up most frequently is the one that has the most number of arrangements.  As the number of dice increases, that random states becomes more and more likely as seen in the above entries for 2, 3 and 4 dice.  Now we jump to 10.

For 10 dice there are over 60 million arrangements (610) and Figure 4 shows the outcomes for 30,000 rolls. This can be compared to Figures 1 to 3.

For ten dice, the chance of a number lower than 20 or greater than 60 is negligible.  The chance of rolling 10 one’s is one over 60 million. The most random states are dominating.  This is only for 10 dice. Next case will be Avogadro’s dice which have 61023 states, which is a lot more than 60 million.

Figure 1

Figure 2

Figure 3

Figure 4

The interactive software used in this video is part of the General Chemistry Tutorial and General Physics Tutorial, from MCH Multimedia. These cover most of the topics found in AP (Advanced Programs in High School), and college level Chemistry and Physics courses.