Statistical Mechanics and Thermodynamics of a Rotating Continuous-Helicity Gas

In this paper, we investigate the thermodynamics of an ideal gas of classical particles with continuous helicity in three-dimensional Minkowski space. Using the one-particle distribution function for a particle with continuous helicity, we derive expressions for the chemical potential, angular momentum, and entropy of the gas. We show that such a system, when placed in a rotating container, can exist in two phases: rotating and non-rotating. We describe the conditions for the phase transition and examine the phase diagram of the gas. It is found that at comparably low angular velocities the rotating phase can exist only in the form of metastable states. A distinctive feature of these metastable states at such low angular velocities is a negative angular momentum.