Statistical Mechanics · Problem 1.2

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · entropy-additivity-omega-multiplicativity

Problem

Assuming that the entropy

S

and the statistical number

\Omega

of a physical system are related through an arbitrary functional form

S = f(\Omega),

show that the additive character of

S

and the multiplicative character of

\Omega

necessarily require that the function

f(\Omega)

be of the form (1.2.6).