Blundell Thermal Physics · Problem 14.8

Entropy

Physics — Statistical Mechanics · entropy-boltzmann-probability

Problem

The probability of a system being in the

i

th microstate is

P_i = e^{-\beta E_i}/Z, \tag{14.56}

where

E_i

is the energy of the

i

th microstate and

\beta

and

Z

are constants. Show that the entropy is given by

S/k_\mathrm{B} = \ln Z + \beta U, \tag{14.57}

where

U = \sum_i P_i E_i

is the internal energy.