  A new approach to the proof of the Arrhenius formula of kinetic theory is
proposed. We prove this formula starting from the equation of diffusion in a
potential. We put this diffusion equation in the form of evolutionary equation
generated by some Schroedinger operator. We show that the Arrhenius formula for
the rate of over the barrier transitions follows from the formula for the rate
of quantum tunnel transitions for the considered Schroedinger operator.
Relation of the proposed approach and the Witten method of the proof of the
Morse inequalities is discussed. In our approach the Witten spectral
asymptotics takes the form of the low temperature limit and the Arrhenius
formula is a correction to the Witten asymptotics.
