Which physicist gave entropy its statistical definition, carved on his gravestone?

Boltzmann, whose formula S = k log W is on his memorial in Vienna's central cemetery - though he never wrote it in that form himself; Planck did, and Planck also named the constant after him.

The equation says something quietly radical: entropy is a count. W is the number of microscopic arrangements consistent with the large-scale state you observe, so a tidy state is one with few arrangements and a disordered one has astronomically many. The second law then stops being a law of nature and becomes a statement about probability - things move towards disorder because there are overwhelmingly more ways to be disordered, and a broken cup could reassemble, it just will not.

The atomism was the fight of his life. Ostwald and Mach held that atoms were a convenient fiction, and Boltzmann spent decades defending the reality of things nobody could see. He killed himself in 1906, while on holiday with his family, in a depression that his colleagues attributed partly to that opposition - and Perrin's measurements confirming atoms came a few years later. The story is probably too tidy: he had suffered severe mood swings for years and by 1906 his position was in fact winning.