Thermodynamics of rotating fermions

We consider the thermodynamic properties of a rotating gas of free fermions. We begin by constructing the thermodynamic potential Φ and its associated current ϕ μ within the grand canonical ensemble of a macroscopic rigidly rotating body, where the ensemble parameters are the temperature T 0 and chemical potential μ 0 on the rotation axis, as well as the rotation angular velocity Ω 0 . We then consider the problem of local thermodynamics, where the thermodynamic state is defined by the local temperature T and chemical potential μ , as well as the local spin potential tensor, Ω μν . We find the thermodynamic pressure P , given as the sum of the usual classical (non-quantum) pressure and other corrections due to the spin potential and the kinematic state of the fluid, based on the local expectation value of the energy-momentum tensor. We compute the associated entropy, charge and spin densities, and show they are consistent with the Euler relation.