Theoretical Model for Time Evolution of an Electron Population under
  Synchrotron Loss
  Many astrophysical sources radiate via synchrotron emission from relativistic
electrons. The electrons give off their kinetic energy as radiation and this
radiative loss modifies the electron energy distribution. An analytical
treatment of this problem is possible in asymptotic limits by employing the
continuity equation. In this article, we are using a probabilistic approach to
obtain the analytical results. The basic logic behind this approach is that any
particle distribution can be viewed as a probability distribution after
normalizing it (as is done frequently in statistical mechanics withi ensembles
containing very large number of particles). We are able to reproduce the
established results from our novel approach. Same approach can be applied to
other physics problems involving spatial or temporal evolution of distribution
functions.
