Vacuum Radiation,Entropy, and Molecular Chaos

Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t ^1/2, and the fractional changes in momentum and energy are proportional to t ^−1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change in momentum of a particle in a gas is very small. However, at the end of the mean free path each particle undergoes an interaction that magnifies the preceding change, and the net result is that the momentum distribution of the particles in a gas is randomized in a few collision times. In this way the random action of vacuum radiation and its subsequent magnification by molecular interaction produces entropy increase. This process justifies the assumption of molecular chaos used in the Boltzmann transport equation.