**Calculation**

The configurational entropy is related to the number of possible configurations by Boltzmann's entropy formula

where *k*_{B} is the Boltzmann constant and *W* is the number of possible configurations. In a more general formulation, if a system can be in states *n* with probabilities *P*_{n}, the configurational entropy of the system is given by

which in the perfect disorder limit (all *P*_{n} = 1/*W*) leads to Boltzmann's formula, while in the opposite limit (one configuration with probability 1), the entropy vanishes. This formulation is analogous to that of Shannon's information entropy.

The mathematical field of combinatorics, and in particular the mathematics of combinations and permutations is highly important in the calculation of configurational entropy. In particular, this field of mathematics offers formalized approaches for calculating the number of ways of choosing or arranging discrete objects; in this case, atoms or molecules. However, it is important to note that the positions of molecules are not strictly speaking *discrete* above the quantum level. Thus a variety of approximations may be used in discretizing a system to allow for a purely combinatorial approach. Alternatively, integral methods may be used in some cases to work directly with continuous position functions.

A second approach used (most often in computer simulations, but also analytically) to determine the configurational entropy is the Widom insertion method.

Read more about this topic: Configuration Entropy

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### Famous quotes containing the word calculation:

“Common sense is the measure of the possible; it is composed of experience and prevision; it is *calculation* appled to life.”

—Henri-Frédéric Amiel (1821–1881)

““To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the *calculation* of Neptune from the observed vagaries of the orbit of Uranus.”

“And yours,” said the P.B.”

—Samuel Beckett (1906–1989)