  We show that the mathematical form of the information measure of Fisher's I
for a Gibbs' canonical probability distribution (the most important one in
statistical mechanics) incorporates important features of the intrinsic
structure of classical mechanics and has a universal form in terms of "forces"
and "accelerations", i.e., one that is valid for all Hamiltonian of the form
T+V. If the system of differential equations associated to Hamilton's canonical
equations of motion is linear, one can easily ascertain that the Fisher
information per degree of freedom is proportional to the inverse temperature
and to the number of these degrees. This equipartition of I is also seen to
hold in a simple example involving a non-linear system of differential
equations.
