Entropy
A measure of the number of microscopic arrangements consistent with a system's macroscopic state. The second law of thermodynamics says it always increases over time.
Entropy is a measure of the number of distinct microscopic arrangements (microstates) that produce the same observable macroscopic state. The second law of thermodynamics states that in an isolated system, entropy never decreases — explaining why heat flows from hot to cold, ice melts in warm rooms, and broken eggs don't reassemble themselves.
Mathematically, entropy is given by S = k ln(W), where W is the number of microstates and k is Boltzmann's constant.
Entropy is also intimately connected to information theory — Shannon's information entropy uses the same mathematics. The connection extends to black hole physics, where the Bekenstein-Hawking entropy proportional to a black hole's surface area suggests deep links between gravity, thermodynamics, and information.