Second law of thermodynamics

The second law of thermodynamics states that natural processes have a preferred direction. In its most general form it asserts that the total entropy of an isolated system — or of the universe — never decreases: ΔS_universe ≥ 0, with equality only for an idealised reversible process and strict increase for every real one.

It has several equivalent formulations. The Clausius statement: heat does not flow spontaneously from a colder to a hotter body. The Kelvin–Planck statement: no cyclic process can convert heat from a single reservoir entirely into work. The Clausius inequality: ∮ dQ/T ≤ 0 for any cycle. Each can be derived from the others, and all express the same underlying constraint on the arrow of time.

The second law is what distinguishes past from future. The first law permits a cup of coffee to reheat itself by drawing warmth from the room, conserving energy perfectly; the second law forbids it, because such a process would lower the entropy of the universe.

The law emerged from Carnot's 1824 engine analysis, was stated explicitly by Clausius (1850) and Kelvin (1851), and was given its modern entropy formulation by Clausius in 1865 — 'the entropy of the universe tends to a maximum' — with Planck and Boltzmann supplying its statistical foundations.