In this study, an analytic derivation is made for the truncated Cauchy-Lorentz velocity distribution experimentally observed in freestanding graphene membranes. Three methods are used and discussed, including the Fokker-Planck-Kolmogorov equation, the maximum nonsymmetric entropy principle, and the Bayesian inference. From these results, a physical mechanism is provided for the non-Gaussian velocity distribution in terms of carbon atom arrangement in freestanding graphene. Moreover, a new theoretical foundation is proposed for future studies of the anomalous dynamics of carbon atoms in graphene membranes.
