"The general connection between energy and temperature may only be established by probability considerations. [Two systems] are in statistical equilibrium when a transfer of energy does not increase the probability."
-- M. Planck
When we put two systems
and
(with N1 and N2 particles, respectively)
into "thermal contact"
so that the (constant) total energy
U = U1 + U2
can redistribute itself randomly between
and
,
the combined system
will, we postulate, obey the FUNDAMENTAL PRINCIPLE -
it is equally likely to be found in any one of its accessible states.
The number of accessible states of
(partially constrained by the requirement that
N1, N2 and
U = U1 + U2 remain constant)
is given by