The discontinuous behavior of this quantity when two substances are mixed is the subject of the Gibbs paradox.
The discontinuous behavior of this quantity when two substances are mixed is the subject of the Gibbs paradox. Boltzmann rigorously defined this quantity for a system as being proportional to the natural logarithm of the number of microstates corresponding to an observed macrostate. The Sackur-Tetrode equation, derived from that definition, allows for this quantity to be calculated for an ideal monatomic gas. In differential form it appears in the definition of Gibbs free energy; its product with absolute temperature is subtracted from enthalpy to correct for energy in the system unavailable to do work. Therefore it is often thought of as the amount of disorder in a system. FTP, name this quantity symbolized "S" that, according to the 2nd Law of Thermodynamics, is always increasing in a closed system.
The discontinuous behavior of this quantity when two substances are mixed is the subject of the Gibbs paradox.
{Entropy}