S = k log W, carved on Boltzmann's gravestone in Vienna's Zentralfriedhof (1877)
Ludwig Boltzmann's link between the macroscopic quantity and a count of microstates
Science · Physics
Entropy
1865
Physics — thermodynamics and statistical mechanics
The thermodynamic quantity measuring how much of a system's energy is unavailable for work and, in Boltzmann's statistical reading, how many microscopic arrangements correspond to the same macroscopic state. Rudolf Clausius coined the word in 1865 from the Greek for "transformation", deliberately shaping it to sound like "energy". The second law of thermodynamics says it never decreases in an isolated system, which is why heat flows from hot to cold, why no engine is perfectly efficient, and why time appears to run one way.
How to spot them
- ▸Coined by Clausius in 1865 from the Greek for 'transformation', to rhyme with 'energy'
- ▸S = k log W, carved on its author's tombstone in Vienna
- ▸The quantity the second law of thermodynamics says never decreases in an isolated system
- ▸Eddington's 'arrow of time'; the reason a smashed cup never reassembles
Key facts
Coined in 1865 from the Greek τροπή, 'transformation', to sound like 'energy' (1865)
Rudolf Clausius's deliberate coinage
The quantity the second law of thermodynamics forbids from decreasing in an isolated system
Hence heat flows hot to cold, and perpetual motion of the second kind is impossible
C. P. Snow's test of scientific literacy in The Two Cultures (1959)
Not knowing the second law, he said, was like never having read Shakespeare
Shannon's 1948 measure of uncertainty in a message, named on von Neumann's advice (1948)
Claude Shannon's information measure, counted in bits
Bekenstein and Hawking showed a black hole's value is proportional to its horizon area (1972–75)
Black-hole thermodynamics, and the temperature of Hawking radiation
Eddington's name for the property that gives time a direction (1928)
'The arrow of time', from The Nature of the Physical World
Key ideas
- Statistically, a system drifts towards the states that can be realised in the most ways; disorder wins simply by being more numerous.
- It is not 'disorder' in any everyday sense — it counts microstates, which is why a freezing liquid can order itself while the total still rises.
Quick-fire facts
- •Rudolf Clausius coined 'Entropie' in 1865, from the Greek for transformation, choosing a word that echoed 'Energie'
- •Its symbol is S and its SI unit the joule per kelvin (J/K)
- •Ludwig Boltzmann's S = k log W is inscribed on his tombstone in the Zentralfriedhof, Vienna; he died by suicide at Duino in 1906
- •The constant k is the Boltzmann constant, named and first written in this form by Max Planck
- •The second law is often stated as: the entropy of an isolated system never decreases
- •C. P. Snow used ignorance of the second law in The Two Cultures (1959) as the scientific equivalent of never having read Shakespeare
- •Claude Shannon's 1948 information entropy has the same mathematical form; von Neumann reputedly suggested the name because nobody really knows what entropy is
- •Jacob Bekenstein and Stephen Hawking showed a black hole's entropy scales with the area of its event horizon, not its volume
- •Living things do not break the second law: they export more entropy than the order they build, as Schrödinger argued in What Is Life? (1944)
- •Arthur Eddington coined 'the arrow of time' for its one-way increase in 1928
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Sources
- Stanford Encyclopedia of Philosophy — Boltzmann's Work in Statistical Physics
- Peter Atkins — Four Laws That Drive the Universe Short authoritative account of the laws of thermodynamics