  Small thermodynamic systems exhibit peculiar behavior different from that
observed in long-scale systems. Non-equilibrium processes taking place in those
systems are strongly influenced by the presence of fluctuations which can be
large. Contributions to the free energy which vanish at the infinite number of
particles limit cannot be neglected and may exert an important influence on the
dynamics. We show that in spite of these important differences, the method of
non-equilibrium thermodynamics still applies when reducing the size of the
system. By using this method, assumption of local equilibrium at the mesoscale
thereby leads to the formulation of a mesoscopic nonequilibrium thermodynamics
from which expressions for the non-equilibrium currents and kinetic equations
for the probability density can be obtained.
