Classical Mechanics

Configurational Entropy

Microstates and macrostates


There are counters, which are blue on one side and red on the other. If the macroscopic description of our state of interest is 88 red on the 4×44\times 4 checkerboard, how many corresponding micro-states are there?

A coin is tossed 8 8 times, and it is noted that the number of heads is 3. 3. How many sequences of coin flips could have led to this result?

There are 15 15 pigeon-holes for 2 2 pigeons. If at most one pigeon can fit inside each hole, how many distinct arrangements are there for the 2 2 pigeons to fit inside the 15 15 holes?

Assume that we can distinguish each pigeon from the others.

There are six distinct boxes, each of which contains a single ball. If there are three red balls and three blue balls, how many distinct arrangements are possible?

There are 5 5 pigeon-holes for 5 5 pigeons. Three of the pigeons are white, and the other two are grey. If each hole can hold at most a single pigeon, how many micro-states are there for the 5 5 pigeons to fit into the 5 hole?

Assume that we can distinguish each pigeon by their color, but cannot distinguish two pigeons of the same color.


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