# Entropy as the basic rule of natural and sociological science - Part (I)

Professor Emeritus, Kyoto University

Representative Kyoto Energy and Environment Research Association

shingu@enekan.jpćhttp://www.enekan.jp/

On the grave of Ludwig Boltzmann in Vienna Central Cemetery one can see the famous inscription of an equation as shown below which reads,

This is one of the monumental works of Boltzmann telling us what is entropy in statistical thermodynamics. This formula tells that entropy, S, is logarithm of the number of states one atom can take (density of states), W, multiplied by a constant k the Boltzmann constant. Since k is a constant if S is normalized by k the equation may simply be expressible as, S = logW, without changing the meaning of the formula.

Although this equation is generally understood as the formula for thermodynamics, since it is a mathematical equation, S may be interpretable as the utility of any number N that belongs to certain object, person or subject one is concerned.

For instance, if N is the number of apples per person, the utility of that thing can be written as,

To understand the meaning of this expression, we must remind ourselves the meaning of logarithm of a number. A short reminder of logarithmic counting method is given below.

Written by Shingu : April 15, 2017 01:56 PM