The problem is simpler in this Maxwellian case than in the more general case of any state of the body in which there is an unequal distribution in space of the molecules.
SECTION B
SIMPLE ANALYTICAL EXPRESSION FOR DEPENDENCE OF ENTROPY ON PROBABILITY
Here also we will dispense with a full proof and content ourselves with the main steps which lead to the desired expression. We will follow PLANCK'S elegant presentation on pp. 136-148 of his Wärmestrahlung. On [p. 22] we have dwelt on the usefulness and the necessity for the probability idea in general physics and in this particular case. We can start, therefore, with PLANCK'S theorem:
"The entropy of a physical system in a particular state depends solely on the probability of this state."
No rigorous proof is here attempted, nor any numerical computations; for present purposes it will suffice to fix in a general way the kind of dependence of entropy on probability.
Let
designate the entropy and
