Entropy

Abstract Entropy is as important a concept as energy, but less well known. The two concepts were first distinguished in the middle of the 19th century. By 1900 entropy was understood to be a measure of disorder and been widely applied in physics and chemistry, but in 1947 it was discovered to be the correct measure of ignorance. In an increasingly data-driven world the ‘principle of maximum entropy’ is playing a key role in data analysis and decision making. Quantum mechanics is a scheme for computing probability distributions, which are quantified by entropy. ‘entanglement entropy’, which plays a key role in cutting-edge quantum technologies, is revealing aspects of entropy that are not evident in the classical world. The thermodynamics of gravitating systems such as star clusters profoundly differs from that of the every-day systems from which entropy emerged. From the thermodynamics of black holes, which involves relativity and quantum mechanics in addition to gravity, an idea, the ‘holographic principle’, emerges that calls into question our current model of material reality. This book traces the emergence of entropy and energy as key concepts and illustrates their practical importance by discussing aspects of the energy transition such as heat pumps, solar cells, carbon capture, and liquified natural gas. Then it explains how entropy quantifies ignorance and illustrates the resulting principle of maximum entropy by reference to image reconstruction. Chapters on the role of entropy in quantum mechanics and gravity follow.