**Entropy** is a concept applied across physics, information theory, mathematics and other branches of science and engineering. The following definition is shared across all these fields:

where *S* is the conventional symbol for entropy. The sum runs over all microstates consistent with the given macrostate and is the probability of the *i*th microstate. The constant of proportionality *k* depends on what units are chosen to measure *S*. When SI units are chosen, we have *k* = *kB* = Boltzmann's constant = 1.38066×10−23 J K−1. If units of *bits* are chosen, then *k* = 1/ln(2) so that .

Entropy is central to the second law of thermodynamics. The second law in conjunction with the fundamental thermodynamic relation places limits on a system's ability to do useful work.

The second law can also be used to predict whether a physical process will proceed spontaneously. Spontaneous changes in isolated systems occur with an increase in entropy.

The word "entropy" is derived from the Greek *εντροπία* "a turning towards" (*εν-* "in" + *τροπή* "a turning").