Planck's formula in classical mechanics
Luigi Galgani
Abstract
We consider the model studied by Poincare'
in connection with Planck's law, when he proved the necessity of quantization,
namely a system of N independent
identical oscillators, each of which interacts through smooth collisions
with a gas
particle (mimicing a heat reservoir),
according to the laws of classical mechanics.
We prove that the expected
energy distribution of the oscillators obeys Planck's formula, i.e. Planck's law
with an action characteristic of the system in place of Planck's constant.
This is obtained by combining two ingredients, namely: the conception of Jeans
who, following a perspective
introduced by Boltzmann, was thinking of Planck's formula as
describing a situation of quasi equilibrium very far from equilibrium, and:
Einstein's conception of the thermodynamic role of
the energy fluctuations,
which is at the basis of nonequilibrium thermodynamics.
In turn, the energy fluctuations are estimated by the
most advanced mathematical results presently available
for the energy exchanges in elementary collision processes.
Elenco dei partecipanti al convegno di Bari.