From Quantum Tsallis Entropy to Strange Metals

Abstract: We develop a unified framework connecting quantum Tsallis statistics to electronic transport in strongly interacting systems. Starting from R\'enyi and Tsallis entropies, we construct a quantum Tsallis distribution that reduces to the conventional Fermi--Dirac distribution when $q=1$. For $q$ slightly deviating from unity, the correction term in the occupation function can be mapped to a $q$-deformed Schwarzian action, corresponding to soft reparametrization modes. Coupling these soft modes to electrons via the Fermi Golden Rule yields a modified scattering rate, which reproduces conventional Fermi-liquid behavior at low temperatures and linear-in-temperature resistivity at high temperatures. Using the memory matrix formalism, we analyze magnetotransport, finding a linear-in-field magnetoresistance and a Hall angle consistent with Anderson's two-lifetime scenario. At sufficiently low temperatures, both magnetoresistance and Hall response smoothly recover Fermi-liquid quadratic behaviors. This approach provides a controlled interpolation between Fermi-liquid and non-Fermi-liquid regimes, quantitatively linking $q$-deformation, soft-mode dynamics, and experimentally measurable transport coefficients in strange metals.