Fokker-Planck entropic force interpretation of galactic rotation curves

Abstract

We investigate whether the discrepancy between observed galactic rotation curves and those predicted from baryonic matter can be interpreted as the manifestation of an emergent entropic force. Starting from a minimal statistical framework, we derive an effective radial force from a stationary solution of the Fokker-Planck equation under simple and physically motivated assumptions. We confront this Fokker-Planck entropic (FPE) model with high-quality rotation curves from the SPARC database, performing a systematic comparison with standard halo profiles, including Navarro-Frenk-White (NFW), Burkert, and pseudo-isothermal (ISO) models. The FPE model provides fits of comparable or improved statistical quality than traditional profiles, while yielding stellar mass-to-light ratios within physically consistent ranges, in contrast to NFW and Burkert fits that often approach prior limits. Beyond reproducing rotation curves, the model naturally gives rise to strong correlations between its characteristic parameter and global galaxy properties, including the flat rotation velocity and infrared luminosity. These relations are consistent with well-known empirical scaling laws such as the Tully-Fisher relation, suggesting that the proposed framework captures key aspects of the underlying dynamics. Our results indicate that a minimal entropic-force description, grounded in statistical mechanics, can account for galactic rotation curves while simultaneously encoding their scaling relations, offering a complementary and physically motivated perspective to standard dark matter halo interpretations of galaxy rotation curves.