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Entropy: A Very Short Introduction
Very Short Introductions: Brilliant, Sharp, Inspiring
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.
ABOUT THE The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
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.
ABOUT THE The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
- GenresScienceNonfiction
128 pages, Paperback
Published December 29, 2025
About the author
James Binney
9 books8 followersJames Jeffrey Binney, FRS, FInstP (born 1950 in Surrey) is a British astrophysicist. He is a Professor of Physics at the University of Oxford and former head of the Sub-Department of Theoretical Physics as well as a Professorial Fellow at Merton College. Binney is known principally for his work in theoretical galactic and extragalactic astrophysics, though he has made a number of contributions to areas outside of astrophysics as well.
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Displaying 1 - 4 of 4 reviews
March 3, 2026
I had high expectations for this book, but I think that you need some background in mechanical engineering and physics to understand. It is not written for a wider audience. Also, some notions and metaphors are used, but not explained. What does entropy as pollutant means? A pollutant is a harmful substance, but how can entropy (which we determine, not measure) be harmful? Why keep the wrong metaphor of order and disorder, with defining what order or disorder mean? If I have a set of molecules arranged is a non-patterned fashion is a crystal, the arrangement seems without any discernible order, but its “informature” (amount of information), and consequently, its entropy is zero.
Nonetheless, despite the multiple digressions from the argument, it is an interesting book for engineers and physicists.
Nonetheless, despite the multiple digressions from the argument, it is an interesting book for engineers and physicists.
December 10, 2025
The organisation of the book is excellent. The initial chapters are historical, firmly establishing the physical nature of entropy, which is inextricably related to thermodynamics and concepts such as work and Boyle’s law. A qualitative approach is introduced head-on. This approach makes it easy to see the intimate relevance of the concept of entropy to the immediate issue of energy efficiency, which is pivotal in tackling climate change.
Almost seamlessly, the probabilistic perspective of entropy is introduced, culminating in a discussion of Shannon’s derivation of entropy. Importantly, the author reminds the reader: “An increase in entropy is caused by real physical effects, but the increase itself is a statement about the decay of our knowledge base” (p. 57). It is never a purely abstract entity.
It then explores the implications of quantum mechanics and gravity for the concept of entropy, examining the impact on cosmological theories. The maths are decidedly difficult, partly because the book assumes knowledge not only of mathematics but also of physics. My maths and physics are at high-school level, and by profession I am only a medical doctor, so I find much of the maths hard to digest. Yet an overall, if somewhat superficial, understanding is still possible.
Almost seamlessly, the probabilistic perspective of entropy is introduced, culminating in a discussion of Shannon’s derivation of entropy. Importantly, the author reminds the reader: “An increase in entropy is caused by real physical effects, but the increase itself is a statement about the decay of our knowledge base” (p. 57). It is never a purely abstract entity.
It then explores the implications of quantum mechanics and gravity for the concept of entropy, examining the impact on cosmological theories. The maths are decidedly difficult, partly because the book assumes knowledge not only of mathematics but also of physics. My maths and physics are at high-school level, and by profession I am only a medical doctor, so I find much of the maths hard to digest. Yet an overall, if somewhat superficial, understanding is still possible.
June 17, 2026
Useless.
Clips
Maxwell derived four extremely useful identities that make non-trivial statements about how any thermodynamic system will respond to changes. For example one of Maxwell’s relations states that the rate at which a fluid’s temperature falls as its volume is adiabatically expanded is equal to T times the rate at which its pressure rises when it is heated at constant volume. The
Thus if caloric is identified with entropy, we have to drop the dogma that caloric cannot be created: entropy is always created when something happens irreversibly. What entropy has in common with caloric is that it cannot be destroyed.
Water vapour has much higher entropy than liquid water, so water evaporates when the entropic cost L/T of the latent heat L required to evaporate water is lower than the entropy of water vapour, which decreases as its pressure increases. Above 100°C, the entropic cost of thermal energy is less than the entropy of water vapour even at atmospheric pressure, so kettles boil.
When a bosonic gas such as helium is cooled at high density, the response to crowding is very different to that of the electrons in a metal—an ‘electron gas’. At some point a macroscopically large number of atoms accumulates in the least energetic single-particle state. The component comprising these particles has become a ‘Bose-Einstein condensate’ and it flows without viscosity—for this reason it’s called a ‘superfluid’.
electrons repel each other electrostatically, but in a material they can attract each other on account of their ability to distort the crystal lattice. In certain materials pairs of electrons become bound to one another at low temperatures. Each bound pair constitutes a boson, and these newly created bosons form a (charged) superfluid. Consequently currents can now flow without resistance—the material has become superconducting.
From Einstein equations it follows that if at any time the ‘vacuum’ had a non-zero energy density, gravity would become an explosive force that would blast space apart. The theory of inflation is that 13.8 billion years ago this actually happened within a quantum fluctuation of some earlier Universe, and that the Universe we see is a fragment of the vast space into which gravity inflated the original quantum fluctuation. After the tiniest fraction of a second, the energy density of the fluctuation switched from the form that makes gravity repulsive to the familiar forms for which it’s attractive. At this moment a vast quantity of entropy was created because the switch between energy types was irreversible. The Universe became intensely hot and for the next 100,000 years the Universe was dominated by radiation. The expansion of the Universe adiabatically cooled the radiation, and protons and neutrons and later electrons condensed out of the cooling fireball.
Clips
Maxwell derived four extremely useful identities that make non-trivial statements about how any thermodynamic system will respond to changes. For example one of Maxwell’s relations states that the rate at which a fluid’s temperature falls as its volume is adiabatically expanded is equal to T times the rate at which its pressure rises when it is heated at constant volume. The
Thus if caloric is identified with entropy, we have to drop the dogma that caloric cannot be created: entropy is always created when something happens irreversibly. What entropy has in common with caloric is that it cannot be destroyed.
Water vapour has much higher entropy than liquid water, so water evaporates when the entropic cost L/T of the latent heat L required to evaporate water is lower than the entropy of water vapour, which decreases as its pressure increases. Above 100°C, the entropic cost of thermal energy is less than the entropy of water vapour even at atmospheric pressure, so kettles boil.
When a bosonic gas such as helium is cooled at high density, the response to crowding is very different to that of the electrons in a metal—an ‘electron gas’. At some point a macroscopically large number of atoms accumulates in the least energetic single-particle state. The component comprising these particles has become a ‘Bose-Einstein condensate’ and it flows without viscosity—for this reason it’s called a ‘superfluid’.
electrons repel each other electrostatically, but in a material they can attract each other on account of their ability to distort the crystal lattice. In certain materials pairs of electrons become bound to one another at low temperatures. Each bound pair constitutes a boson, and these newly created bosons form a (charged) superfluid. Consequently currents can now flow without resistance—the material has become superconducting.
From Einstein equations it follows that if at any time the ‘vacuum’ had a non-zero energy density, gravity would become an explosive force that would blast space apart. The theory of inflation is that 13.8 billion years ago this actually happened within a quantum fluctuation of some earlier Universe, and that the Universe we see is a fragment of the vast space into which gravity inflated the original quantum fluctuation. After the tiniest fraction of a second, the energy density of the fluctuation switched from the form that makes gravity repulsive to the familiar forms for which it’s attractive. At this moment a vast quantity of entropy was created because the switch between energy types was irreversible. The Universe became intensely hot and for the next 100,000 years the Universe was dominated by radiation. The expansion of the Universe adiabatically cooled the radiation, and protons and neutrons and later electrons condensed out of the cooling fireball.
March 30, 2026
3.7 ⭐
Мабуть, мені треба було трохи уважніше вчити фізику в школі. Це б дуже допомогло при прослуховуванні данного introduction. На деяких частинах кипів мозок, і я була схожа на того котика з мема (в котрого очі в різні боки). Але, заразом з тим, було достатньо цікавих моментів, про які я точно буду згадувати, торкаючись теми вивчення космічного простору та часу в цілому. Як би ж було хоч трохи більше зрозуміло, ех. Але це I`m the problem, а не книжка. Просто не на мій рівень 🙈
Мабуть, мені треба було трохи уважніше вчити фізику в школі. Це б дуже допомогло при прослуховуванні данного introduction. На деяких частинах кипів мозок, і я була схожа на того котика з мема (в котрого очі в різні боки). Але, заразом з тим, було достатньо цікавих моментів, про які я точно буду згадувати, торкаючись теми вивчення космічного простору та часу в цілому. Як би ж було хоч трохи більше зрозуміло, ех. Але це I`m the problem, а не книжка. Просто не на мій рівень 🙈
Displaying 1 - 4 of 4 reviews