Thermodynamics, Conservation Laws and their Rotation Invariance

Abstract

Late in the 1950s, when I developed methods of gasdynamics computations, I, being under the influence of variational principles, arrive at a conclusion that the equations of gasdynamics belong to the class of equations of the following form:

$$ \frac{{\partial {L_{qi}}}}{{\partial t}} + \frac{{\partial M_{{q_i}}^j}}{{\partial {x_j}}} = 0. $$

(1)

On smooth solutions to these equations, one more additional relation holds:

$$ \frac{{\partial \left( {{q_i}{L_{qi}} - L} \right)}}{{\partial t}} + \frac{{\partial \left( {{q_i}M_{{q_i}}^j - {M^j}} \right)}}{{\partial {x_j}}} = 0. $$

(2)

In fact, this relation is a thermodynamic identity.