Lagrangian and Hamiltonian Forms and Their Applications to the Analysis of Heat Conduction

Abstract

Starting from a substantial model of heat conduction, we obtained Lagrangian and Hamiltonian forms in heat conduction, in which the degree of non-equilibrium played an essential role. Next, we explained a general method of analysis and clarified the structure in phase space. Then we applied these techniques to rather difficult problems of heat conduction in solids, demonstrating that they can thus be solved.