However, a paradox arose when attempting to reconcile microanalysis of a system with observations of its macrostate. Many processes are mathematically reversible in their microstate when analyzed using classical Newtonian mechanics. This paradox clearly taints microscopic explanations of macroscopic tendency towards equilibrium, such as James Clerk Maxwell 's 1860 argument that molecular collisions entail an equalization of temperatures of mixed gases. From 1872 to 1875, Ludwig Boltzmann reinforced the statistical explanation of this paradox in the form of Boltzmann's entropy formula, stating that an increase of the number of possible microstates a system might be in, will increase the entropy of the system, making it less likely that the system will return to an earlier state. His formulas quantified the analysis done by William Thomson, 1st Baron Kelvin, who had argued that: