Second Law of Thermodynamics
The law that entropy in an isolated system never decreases, fixing the direction of natural processes and limiting the efficiency of engines.
The second law of thermodynamics states that the entropy of an isolated system never decreases; it either stays constant or increases. Entropy is a measure of the number of microscopic arrangements consistent with a system's macroscopic state — loosely, a measure of disorder — and the law says that natural processes move toward the most probable arrangements. Heat flows spontaneously from hot to cold, gases expand to fill their containers, and a dropped cup does not reassemble itself.
The law has several equivalent formulations. The Clausius statement says heat cannot flow spontaneously from a colder body to a hotter one. The Kelvin–Planck statement says no engine operating in a cycle can convert heat entirely into work; some heat must always be rejected to a cold reservoir. Both formulations follow from the entropy statement, and both express the same content: some processes are thermodynamically irreversible.
The statistical interpretation, developed by Boltzmann, explains why the law holds: macroscopic states compatible with enormously more microscopic configurations are overwhelmingly more likely, and systems left alone move toward them. The entropy of a system is S = k ln W, where k is the Boltzmann constant and W is the number of microstates. The "increase" is not an absolute prohibition but a statement about probabilities so extreme that violations are never observed on macroscopic scales.
The law bounds what technology can do. A heat engine operating between temperatures T_hot and T_cold can convert at most the Carnot efficiency 1 − T_cold/T_hot of the heat input into work; the rest must be discarded. Refrigerators and heat pumps must consume work to move heat "uphill," and any real process that produces useful work also produces some entropy as a byproduct.
Entropy increase provides the thermodynamic arrow of time: it is the only known fundamental law that distinguishes past from future. Local decreases of entropy are possible only at the expense of larger increases elsewhere — a refrigerator cools its interior by heating its surroundings, and an organism maintains its order by consuming energy and producing heat. Information processing itself has a thermodynamic cost, a fact at the heart of Landauer's principle and the physics of computation.