"Thermodynamique cach\'ee des particules" and the quantum potential
  According to de Broglie, temperature plays a basic role in quantum Hamilton-Jacobi theory. Here we show that a possible dependence on the temperature of the integration constants of the relativistic quantum Hamilton-Jacobi may lead to corrections to the dispersion relations. The change of the relativistic equations is simply described by means of a thermal coordinate. 
Marco Matone
hep-ph