Plenary lecture 12: mathematical model and simulations of pedestrian motion in dangerous situations
Vincenzo Ciancio · 2009
Starting from the theory of the energy-momentum tensor, we introduce the four vector density of entropy current in which the entropy density is regarded as function of the energy density and of the symmetric strain tensor. By considering the concept of relativistic equilibrium state, it is defined the temperature in a generic inertial frame obtaining the transformation equations introduced by H. Ott for the temperature and the heat (without postulate Gibbs relation). Moreover, the considerations on the relativistic stress tensor allow us to obtain the transformation equations for the strain tensor. Finally time component of the derivative with respect to the coordinate of the four vector density of entropy current expresses the entropy balance and therefore the entropy production.