Équation de Boltzmann : c'est en introduisant l'hypothèse de **chaos moléculaire**, qui revient ici à dire qu'il n'y a pas de corrélation entre les vitesses entrantes de deux particules en collision, que //la flèche du temps apparait// et que l'on peut montrer que l'entropie augmente, c'est à dire que les systèmes vont vers l'équilibre. Mais cette non-corrélation n'est qu'apparente ! C'est seulement parce que la corrélation est suffisamment diluée et fine-grained qu'elle disparait à nos échelles.

There are various conditions which might apply while a gas expands : 1. adiabatic (isentropic) expansion. Gas does work on its surroundings (pushing on the boundary as the boundary moves) so loses energy. No heat comes in. So internal energy goes down. Temperature goes down. 2. isothermal. Obviously the temperature does not change. This is because heat flows in while the gas does work in expanding. 3. constant enthalpy (Joule-Kelvin process, also known as throttling). The temperature may go up or down, depending on the initial conditions. 4. free expansion (expansion into vacuum). This is a process at constant internal energy. Temperature of an ideal gas stays constant, temperature of a real gas falls a little. This is because the molecules attract one another so as they move apart they gain potential energy. But no energy has come in so they must lose kinetic energy. The kinetic energy is directly related to the temperature.

Observation de stuctures de basse pression intermittentes dans un écoulement turbulent, Pour la Science Avril 96