His version of entropy, expressed concisely by the equation on his tombstone, uses statistical reasoning to provide a link between the hire number of individual ingredients that make up a physical system and the overall properties the system has.⁴
4. To keep the focus on modern ways of thinking about these ideas, I am skipping over some very interesting history. Boltzmann's own thinking on the subject of entropy went through significant refinements during the 1870s and 1880s, during which time interactions and communications with physicists such as James Clerk Maxwell, Lord Kelvin, Josef Loschmidt, Josiah Willard Gibbs, Henri Poincaré, S. H. Burbury, and Ernest Zermelo were instrumental. In fact, Boltzmann initially thought he could prove that entropy would always and absolutely be nondecreasing for an isolated physical system, and not that it was merely highly unlikely for such entropy reduction to take place. But objections raised by these and other physicists subsequently led Boltzmann to emphasize the statistical/probabilistic approach to the subject, the one that is still in use today.
"The Fabric of the Cosmos" - Brian Greene