Careful calculation of thermodynamical functions of tachyon gas
  We analyze several approaches to the thermodynamics of tachyon matter. The
energy spectrum of tachyons $\epsilon_k=\sqrt{k^2-m^2}$ is defined at $k\geq m$
and it is not evident how to determine the tachyonic distribution function and
calculate its thermodynamical parameters. Integrations within the range $k\in
(m,\infty) $ yields no imaginary quantities and tachyonic thermodynamical
functions at zero temperature satisfy the third law of thermodynamics. It is
due to an anomalous term added to the pressure. This approach seems to be
correct, however, exact analysis shows that the entropy may become negative at
finite temperature. The only right choice is to perform integration within the
range $k\in (0,\infty) $, taking extended distribution function $f_\epsilon =1$
and the energy spectrum $\epsilon_k=0$ when $k<m$. No imaginary quantity
appears and the entropy reveals good behavior. The anomalous pressure of
tachyons vanishes but this concept may play very important role in the
thermodynamics of other forms of exotic matter.
