On Lagrangian and Eulerian interpretations of the local equilibrium assumption in nonequilibrium convective systems
The formulation of nonequilibrium thermodynamics with convective flow under the influence of external potential field is made from the two view points of Lagrangian and Eulerian. Specifying two meanings of the local equilibrium assumption, we define two sets of the thermodynamic forces and fluxes, and derive two evolulion criteria in each picture.
A method of solving the eikonal equation, in either flat or curved space–times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front singularities that are associated with their level surfaces (the characteristic surfaces or “big wave fronts”).