Classical field theory and stochastic properties of hyperbolic equations of dissipative processes

The set of damped hyperbolic transport equations is one of the wide class o f equations for the description of dissipative physical processes. Deeper u nderstanding into the structure of these physical phenomena can be obtained with the help of the Hamiltonian formalism. Tn the present paper, we show that the Hamilton-Lagrange formalism can be constructed for these kinds of transport equations. We obtain the Hamiltonian, the canonically conjugate q uantities and the Poisson-bracket expressions for them. With this formalism we analyze the statistical properties of path fluctuations in the new conj ugated thermodynamic variable space. We show that for short times the stoch astic behavior under this new scope obeys the Chapman-Kolmogorov relationsh ip. (C) 1999 Elsevier Science B.V. All rights reserved.