Artículo de revista
Hamiltonian formalism and path entropy maximization
Fecha
2015Registro en:
Journal of Physics A-Mathematical and Theoretical Volumen: 48 Número: 42 oct 2015
1751-8113
DOI: 10.1088/1751-8113/48/42/425003
Autor
Davis, Sergio
González, Diego
Institución
Resumen
Maximization of the path information entropy is a clear prescription for constructing models in
non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the
assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges
which determines the most probable trajectory. Deviations from the probability maximum can be
consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation
and its associated Fokker-Planck equation. The connections unveiled between the maximization of
path entropy and the Langevin/Fokker-Planck equations imply that missing information about the
phase space coordinate never decreases in time, a purely information-theoretical version of the
Second Law of Thermodynamics. All of these results are independent of any physical assumptions,
and thus valid for any generalized coordinate as a function of time, or any other parameter. This
reinforces the view that the Second Law is a fundamental property of plausible inference.