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Entropy of rolling a dice assuming to be a micro canonical ensemble is given by :

I know $S = K \space ln \space\Omega $ but how to find $\Omega$ ( No. of ways in which dice can arrange itself ) ?

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If you have one "die" (singular of the plural "dice") and all you care about is which face is up, then the number of microstates is the number of faces. For example, for a six-sided die, $\Omega=6$. In the real world, a die's microstates would also involve knowing its position and orientation, at least, but in conceptual discussions, people usually just treat an $n$-sided die as being a degree of freedom with $n$ discrete states.

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  • $\begingroup$ Thank You so much $\endgroup$ Aug 21 at 5:05
  • $\begingroup$ You're welcome! $\endgroup$
    – David
    Aug 21 at 22:58

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