  Recently, a morphological transition in the velocity distribution of a
relativistic gas has been pointed out which shows hallmarks of a critical
phenomenon. Here, we provide a general framework which allows for a
thermodynamic approach to such a critical phenomenon. We therefore construct a
thermodynamic potential which upon expansion leads to Landau-like (mean-field)
theory of phase transition. We are therefore able to calculate critical
exponents and explain the spontaneous emergence of order parameter as a result
of relativistic constraints. Numerical solutions which confirm our
thermodynamic approach are also provided. Our approach provides a general
understanding of such a transition as well as leading to some new results.
Finally, we briefly discuss some possible physical consequences of our results
as well as considering the case of quantum relativistic gases.
