Hamilton’s Principle for a Set of Nonlinear Heat Conduction

We calculate the Lagrangian for certain type of differential equations of nonlinear heat conduction, applying potential function method introduced previously. On the other hand, we point out that these kind of nonlinear parabolic differential equations describe Markovian processes in a new phase space.

[1]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[2]  Till D. Frank.  A note on the Markov property of stochastic processes described by nonlinear Fokker–Planck equations , 2003 .

[3]  K. Martinás,et al.  Examination of phenomenological coefficient matrices within the canonical model of field theory of thermodynamics , 1997 .

[4]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[5]  F. Márkus,et al.  Onsager's regression and the field theory of parabolic transport processes , 2003 .

[6]  Lars Onsager,et al.  Fluctuations and Irreversible Processes , 1953 .

[7]  Robert Graham,et al.  Fluctuations and nonlinear irreversible processes. II , 1979 .

[8]  J. Kirkwood.  The Statistical Mechanical Theory of Transport Processes I. General Theory , 1946 .

[10]  Lars Onsager,et al.  Fluctuations and Irreversible Process. II. Systems with Kinetic Energy , 1953 .

[11]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[12]  Melville S. Green,et al.  Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena , 1952 .

[13]  Robert Graham,et al.  Path integral formulation of general diffusion processes , 1977 .

[14]  F. Márkus,et al.  Hamilton-Lagrange formalism of nonequilibrium thermodynamics. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Peter Hänggi,et al.  Stochastic processes: Time evolution, symmetries and linear response , 1982 .

[16]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[17]  F. Vázquez,et al.  Classical field theory and stochastic properties of hyperbolic equations of dissipative processes , 1999 .