Note on the thermodynamics and the speed of sound of a scalar field
  We investigate the correspondence between a perfect fluid and a scalar field
and show a possible way of expressing thermodynamic quantities such as entropy,
particle number density, temperature and chemical potential in terms of the
scalar field phi and its kinetic term X. We prove a theorem which relates
isentropy with purely kinetic Lagrangian. As an application, we study the
evolution of the gravitational potential in cosmological perturbation theory.
