To exercise our definition we calculate the change in entropy through an
adiabatic free expansion of n moles of a gas at temperature, T from volume
to volume 
. Since temperature of the initial and final states are the same
we have
We see that the change in entropy is positive if the volume increases and negative
if it decreases. Quite generally it turns out that
the sign of the change in entropy
will function as our ``arrow of time''. Specifically the second law of thermodynamics states
that
for any spontaneous thermodynamic process in a closed system.
We can be even more specific since a closed system is characterized by
Thus entropy for a closed system can only increase and it does so
for irreversible processes while entropy is unchanged
for reversible processes.