"A Hamiltonian Formulation for the Diffusion Equation"
A Hamiltonian formulation is presented for the diffusion equation.
Going beyond the conservation of property in diffusive transport,
conservation is shown to apply in the sense
of classical Hamiltonian dynamics, provided the equation is
transformed with Hermitian wavelets. The characteristic
equations, obtained previously for the wavelet-transformed diffusion
equation, are the canonical equations corresponding to a time-independent
Hamiltonian. The configuration variables are defined by the
canonical structure and its invariants, while the momenta determine
the evolution of the system. Irreversibility results from the
finite-time escape of trajectories, initiating from the smallest scales
and eroding increasingly larger scales. However, this scale-dependent erosion
of initial conditions does not necessarily imply memory loss.
Physical Review E 55,1590-1599 (1997).
Jacques Lewalle, firstname.lastname@example.org