His father, Ludwig Georg Boltzmann, was a tax official. But his father died when he was 15 yrs. old. Boltzmann studied physics at the University of Vienna, starting in 1863. Boltzmann was awarded a doctorate from the University of Vienna in 1866 for a thesis on the kinetic theory of gases supervised by Josef Stefan. After obtaining his doctorate, he became an assistant to his teacher Josef Stefan.
He established the relationship between entropy and probability was first stated in his kinetic theory of gases". Entropy is a measure of the disorder of a system, where S is the entropy, k is Boltzmann's constant, and W is the number of states accessible to the system. Boltzmann first wrote down his equation in 1872.
Boltzmann’s scientific approach was to attack the problem. He explained the second law of thermodynamics in the early 1870s on the basis of the atomic theory of matter. He demonstrated that the second law could be interpreted by blending the laws of mechanics, applied to the motions of the atoms, with the theory of probability. He clarified that the second law is an essentially statistical law. The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law. In particular, it was his attempt to reduce it to a stochastic collision function, or law of probability following from the random collisions of mechanical particles.
He also derived the "H-theorem " and Boltzmann equation in his paper of 1872. The H-theorem