Past research has found a strong analogy between meandering river systems and thermodynamics. In this study we verify the first law of thermodynamics which is applied to meandering rivers by quantifying the curvature frequency balance. Thus, both the amalgamation process (i.e. lower curvature scales joining to give birth to higher curvature scales) and the splitting process (i.e. higher curvature scales being split into lower ones) are quantified. We also evaluate the second law of thermodynamics for meandering systems by estimating the yearly Shannon negentropy. Likewise, we propose a meandering classification scheme that is based on: [1] the yearly negentropy gradient, and [2] a quantitative continuum of the degree of confinement, which is estimated from the Frechet distance between the meandering centerline curvature and that of the mean center. Thus, we believe that our meandering classification scheme has the potential to complement the prevailing observational Brice classification scheme.