The Boltzmann equation

 Ludwig Boltzmann

Portrait of Boltzmann at age 31

Ludwig Boltzmann (1844–1906) pioneered the concept that entropy could be calculated by examining the positions and energies of molecules. He developed an equation, known as the Boltzmann equation, which relates entropy to the number of microstates (W):

S = k ln W

where k is the Boltzmann constant (1.38 x 10^-23 J/K), and W is the number of microstates.

Microstates is a term used to describe the number of different possible arrangements of molecular position and kinetic energy at a particular thermodynamic state.  A process that gives an increase in the number of microstates therefore increases the entropy.