It is perhaps not obvious from our definition of entropy
but this state function is in fact a measure of the degree
of disorder. This is perhaps best illustrated by the
example of the adiabatic free expansion of a gas: There is greater order
when the gas is confined to a smaller volume. Disorder grows as does entropy
if we allow the gas to occupy a larger volume. This interpretation
is most apparent in in Boltzmann's formula for entropy.
In this formula which is consistent with Eq. 1, W is the number
of micro-states which correspond to the specific macro-state specified
by the relevant thermodynamic variables. We now clearly see that entropy
is a measure of microscopic disorder
specifically how many micro states of the systems are indistinguishable
in a macroscopic description of the system.