Statistical structure of canonical kinetic equilibrium with sheared flow

In isothermal kinetic equilibrium of a plasma with sheared flow, the electrostatic potential is the cumulant generating function of the velocity distribution, encoding all non-Maxwellian statistics. Consequently, of the polynomial-form flux-function equilibrium flows, only the linear one is admissible, and every other equilibrium sheared flow has non-zero cumulants to all orders. The identity is shown for a sheared-flow screw pinch and specialized to the Z pinch, theta pinch, and Harris sheet. A simple sheared-flow Bennett pinch illustrates the principal results, namely weaker magnetization yields more non-Maxwellian features, and co- and counter-current flow shear have distinct statistics. The identity also yields a method for initializing kinetic simulations.