Exotic quantum statistics from a many-body theory of Majorana fermions

Starting with a simple counting argument, we construct a statistical and thermodynamic model of free Majorana fermions at low temperature. Originally defined as a fermion identical to its own antiparticle state, Majorana particles often appear in the contemporary many-body literature as non-Abelian zero energy modes in topological superconductors. We deviate from the usual anyonic description and instead consider a gas of non-interacting, spin-1/2 Majorana fermions as Ettore Majorana first envisioned them. A combinatorial analysis of the many-body Majorana ensemble leads to a configurational entropy which deviates from the fermionic result with an increasing number of available microstates. A Majorana distribution function is derived which shows signatures of a sharply-defined Fermi surface at finite temperatures. The Majorana distribution is then re-derived in the context of a modified Kitaev chain with bosonic pair interaction. The thermodynamics of the free Majorana system is found to be nearly identical to that of a free Fermi gas, except now distinguished by a two-fold ground state degeneracy and, thus, a residual entropy at zero temperature. Experimental realization of the Majorana thermodynamics is then discussed in the context of real materials and cosmological phenomena.