sci.physics.research

I have discovered a simple and amazing result, a surprising
consequence of the maximum entropy principle, and would like to know
if it is true or not. Here it is:

Mathematically, from the set of constraints (p_i reads p with indice
i, sums are over all values of i):
I = sum (-p_i ln p_i) maximum
x = sum (p_i * x_i)
t = sum (p_i * t_i)
one can deduce, using Lagrange multipliers, that:
L = dI/dt satisfies d°L/d°x = (d/dt)d°L/d°(x_dot) where d°
means partial differential and x_dot==dx/dt.

L has the property of the Lagrangian in physics. Up to a
multiplicative constant of dimension Action, L is the Lagrangian, I
the action, the Lagrange multiplier of the (generalised) coordinates
are the (generalised) momenta, and the Lagrange multiplier of the time
is the opposite of the Hamiltonian. All Lagrangian mechanics can be
deduced from this set of constraints.

A detailed demonstration can be found at /hal-00123252/en/

It means that all lagrangian mechanics can be deduced from:
1/ the hypothesis (more natural, I think, that the least action
principle) that all we know is an average path in spacetime
coordinates.
2/ the use of Maxent, which is justified by the repeatability of the
experiment.

Could anyone confirm (or infirm) this fact?