Until the middle of the nineteenth century entropy and energy were confused with one another. The intellectual fog slowly cleared and now these words name subtle and powerful concepts. Most people think they know what energy is, but few could define entropy.

This Very Short Introduction traces the emergence of entropy and energy as distinct concepts, and explains how entropy spread from thermodynamics into statistical mechanics, probability theory and data science. It explains the implications of entropy for heat pumps, solar cells, carbon capture, and liquified natural gas. Quantum mechanics and gravity open new horizons for entropy, and when combined in the quantum theory of black holes, they call into question our current understanding of material reality.