In thermodynamics, the formula S = k ln W, called the "Boltzmann formula" or Boltzmann entropy formula, where S is the entropy of an ideal gas system, k is the Boltzmann constant, equal to 1.38062 x 10E-23 joule/kelvin, and W is the number of “states” the particles of the system can be found in according to the various energies with which they may each be assigned, is a popular statistical representation of the entropy of a system in which the particles have uncorrelated velocities. Some consider S = k ln W to be easily the second most important formula of physics, next to E = mc² or at par with it. [1]

The formula is a modified or reduced form of Austrian physicist Ludwig Boltzmann's H-function and was first put in this shorthand form by German physicist Max Planck in his 1901 paper “On the Law of Distribution of Energy in the Normal Spectrum.” [1] Specifically, Planck explains that the entropy SN of the system [resonator] is proportional to the logarithm of its probability W, within an arbitrary additive constant:

S = k log W + const

This formula is famously displayed on the Boltzmann tombstone, which was erected in the 1930s, at the Central Cemetery (Zentralfriedhof), Vienna, Austria. [2] At some point the switch from base 10 logarithms to base e natural logarithms began to be used.

In human thermodynamics, Boltzmann's entropy formula is used to model the entropy of any number of anthropomorphic quantities or qualities, with unabandon, in nearly every scenario or situation conceivable.

References
1. (a) Planck, Max. (1901). “On the Law of Distribution of Energy in the Normal Spectrum.” Annalen der Physik, Vol. 4, pg. 553 ff.
(b) Muller, Ingo. (2007). A History of Thermodynamics - the Doctrine of Energy and Entropy, (ch. 4: "Entropy as S = k ln W," pg. 101-02). New York: Springer.
2 (a) Planck, Max. (1901). “On the Law of Distribution of Energy in the Normal Spectrum,” Annalen der Physick, Vol. 4, pg. 553 ff.
(b) Schmitz, John E.J. (2007). The Second Law of Life: Energy, Technology, and the Future of Earth as We Know It, (pg. 83). William Andrew Publishing.
(c) Boltzmann equation – Eric Weisstein’s World of Physics (states the year was 1872).
3. Photo of Boltzmann tomb (Vienna, 2005)