Irreversibility and Entropy Exclusion in Collisionless Plasmas

We examine entropy production in reduced descriptions of collisionless plasmas. Introducing a closure dependent entropy hierarchy, we show that non-conservative moment closures generate a residual entropy associated with irreversible information loss, whereas invariant closures remain reversible. The monotonic growth of this residual entropy imposes a statistical realizability constraint on macroscopic plasma states, excluding regions of phase space independent of dynamical stability. For anisotropic plasmas, we evaluate entropy production within a second-order moment closure, identifying contributions from transport and magnetic field inhomogeneity. The resulting entropy exclusion boundary is broadly consistent with observed anisotropy distributions in space plasmas. Statistical realizability thus emerges as an organizing principle for reduced collisionless plasma descriptions.