Careful calculation of thermodynamical functions of tachyon gas

TL;DR

This paper investigates the thermodynamics of tachyon matter, proposing a correct integration approach that ensures physical consistency and avoids negative entropy, with implications for exotic matter thermodynamics.

Contribution

It introduces a revised method for calculating tachyon thermodynamics that ensures positive entropy and eliminates imaginary quantities, improving upon previous approaches.

Findings

Proper integration range yields consistent thermodynamical functions.

Entropy remains positive at finite temperature with the new approach.

Anomalous pressure of tachyons vanishes under correct calculation.

Abstract

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.