  Boltzmann's first paper (1866) in statistical physics aimed to reduce the second law to mechanics. Within the next two years he became acquainted with Maxwell's papers on gas theory of 1860 and 1867, which introduced probability notions in the description of the gas. Maxwell had studied specific mechanical models for a gas (as a system of hard spheres (1860) or of point particles exerting a mutual force on each other inversely proportional to the fifth power of their distance), and characterized the state of such a gas by means of a probability distribution f over the various values of the molecular velocities \(\vec{v}\). For Maxwell, the probability \(f(\vec{v})d^3\vec{v}\) denoted the relative number of particles in the gas with a velocity between \(\vec{v}\) and \(\vec{v} + d^3\vec{v}\).  In particular, he had argued that the state of equilibrium is characterized by the so-called Maxwell distribution function: 