Binney, James Entropy: A Very Short Introduction Oxford University Press 128 pages, 4.33 x 6.89 inches ISBN: 978-0198901488
James Jeffrey Binney
On Entropy: A Very Short Introduction
Interview of
January 21, 2026
In a nutshell
Entropy is a concept that's almost as important as energy, but far less widely understood. The book explains how until the 1850s the two concepts were confused, and that a clear understanding of what entropy really is was reached only in 1947.
A French military engineer, Sadi Carnot, took he first step by thinking clearly about steam engines. For almost two decades his work was neglected, and then it impeded the efforts of an English brewer, James Joule, to establish the concept of energy. Eventually a couple of Germans and a Scotsman made energy and entropy into well defined structures. Over the next fifty years an Austrian and an American made the connection between entropy and disorder. The final step was taken by a mathematician at Bell Labs working on telecommunication protocols.
Today entropy is a hot topic in research into quantum information, black-hole physics and quantum field theory. Entropy is a measure of missing information and quantum systems tend to leak information to their environments through the phenomenon of entanglement. Quantum technologies are concerned with limiting this leakage.
A black hole sets an upper limit on the entropy any body can have. Black holes contain stupendous quantities of entropy, but their entropies don't increase with mass as rapidly as predicted by quantum field theory. Our current understanding of material reality is based on quantum field theory, so entropy is signalling a fundamental weakness in our understanding of the Universe.
The wide angle
Entropy is both a property of matter and a device for selecting probability distributions in light of data. Hence it's an enormously useful tool that should be widely understood. The book explains how entropy gives insight into several aspects of the energy transition, and even had an impact on the course of the 1914-18 war. As a key tool of data processing, its importance is increasing as the world digitises.
Politicians speak of energy as a single, undifferentiated thing: electricity and gas are both sold by the kilowatt hour. But electricity is more valuable than gas because it is energy that is free of entropy. Vast quantities of energy are contained in the Earth's atmosphere and oceans, but this energy is unsaleable because it's heavily polluted with entropy. A heat pump is a device for increasing the quality of free, heavily polluted energy by adding entropy-free energy drawn from the electricity grid. The heat engines found in power stations, cars and aeroplanes produce entropy-free energy from energy that's moderately polluted with entropy by disposing of the undesired entropy in `waste heat'. Carnot already determined the minimum amount of heat that must be discarded to deliver a unit of pure energy. Real engines discard more than this minimum but over the nearly two centuries since Carnot, engineers have edged steadily closer to Carnot's minimum. A solar cell is ultimately a heat engine and subject to Carnot waste-heat formula.
We import an increasing fraction of our natural gas in liquid form. This trade involves pumping most of the entropy out of the gas before it's shipped, and then putting the entropy back in when the ship arrives. These steps are expensive, and Carnot's work tells us that a big opportunity is lost when current plants return the entropy.
A close-up
The story of Sadi Carnot is captivating - the young military engineer with no hope of advancement on account of a notorious father, who established wonderfully general results by pure thought. A genius who died before anyone understood his work. Almost as remarkable is that of brewer James Joule whose hobby was experimental physics, and for almost a decade presented demonstrations that heat is a form of energy to the British Association, only to met with disbelief. Fortunately, three very young professors did take Joule's point and the science of `thermodynamics' was born. It revolutionised chemistry and facilitated the rapid growth of chemical industries in the second half on the 19th century.
The fundamental laws of physics are almost all time reversible: if something changes from A to B, the laws permit B to change to A. Yet our everyday experience is of irreversible events: spilt milk will never jump back into the jug; a bullet will never fly back into the muzzle of the gun; an apartment block shattered by a missile will never pull back together and send the missile back to the truck that launched it. Entropy explains why in practice these processes go in only one direction. In principle they could go backwards, but the probability that they will do so is absurdly small.
In everyday life things settle down once they have reached the state that maximises their entropy given their energy: tea goes cold; things slid on a table come to rest; ripples in a tub of water fade away. What keeps life and the Universe going is a remarkable property of gravity: a system bound by gravity can always achieve higher entropy on a fixed energy budget. This principle drives the evolution of the Sun and of our Galaxy.
Lastly
I hope intelligent readers of all ages and occupations will gain an understanding of a sublimely beautiful and powerful idea. I hope they will start to look at the world around them from an entropic perspective, and to wonder how a mathematical measure of ignorance can so often seem an intrinsic property of matter. I hope they will enjoy reading about the remarkable men who uncovered the existence of entropy and gain insight into how science develops: through steps of varied length, sometimes backwards, always amid doubt and debate. I hope the chapters on quantum physics and black holes will give insight into how the scientific community continues to stumble forward on the research frontier.
Our civilisation is now totally dependent on advanced technologies, which have at their base concepts such as energy and entropy that are very poorly understood by the great majority of people. This is a shame because these are wonderful ideas that enrich your appreciation of what's going on around you. There's poetry in them as well as power.
