Information geometry of boost-agnostic statistical physics

Abstract

The information geometry associated with the Lifshitz ideal gas is studied in the boost-agnostic case (i.e., without assuming boost invariance). Families of geodesics and intrinsic and extrinsic curvatures of the associated Fisher metric are computed. The isobar, isotherm, isochor, and adiabat are recognized as geodesics at lowest order in the fluid velocity. The leading correction is computed, revealing critical behavior in certain regimes of the dynamical critical exponent, z. The intrinsic curvature diverges at T = 0, showing no finite-temperature phase transition. The zero-momentum-exchange submanifold is embedded with vanishing extrinsic curvature and the non-zero velocity submanifold with extrinsic curvature scaling as T^–1.