entropy

English

Etymology

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First attested in 1867, as the translation of German Entropie, coined in 1865 by Rudolph Clausius in analogy to Energie (energy), replacing the root of Ancient Greek ἔργον (érgon, work) by Ancient Greek τροπή (tropḗ, transformation)).

Pronunciation

• IPA(key): /ˈɛntɹəpi/
•  Audio (US) (file)

Noun

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entropy (countable and uncountable, plural entropies)

1. ()
1. strictly thermodynamic entropy. A measure of the amount of energy in a physical system that cannot be used to do work.
The thermodynamic free energy is the amount of work that a thermodynamic system can perform; it is the internal energy of a system minus the amount of energy that cannot be used to perform work. That unusable energy is given by the entropy of a system multiplied by the temperature of the system. (Note that, for both Gibbs and Helmholtz free energies, temperature is assumed to be fixed, so entropy is effectively directly proportional to useless energy.)
2. A measure of the disorder present in a system.
Ludwig Boltzmann defined entropy as being directly proportional to the natural logarithm of the number of microstates yielding an equivalent thermodynamic macrostate (with the eponymous constant of proportionality). Assuming (by the fundamental postulate of statistical mechanics), that all microstates are equally probable, this means, on the one hand, that macrostates with higher entropy are more probable, and on the other hand, that for such macrostates, the quantity of information required to describe a particular one of its microstates will be higher. That is, the Shannon entropy of a macrostate would be directly proportional to the logarithm of the number of equivalent microstates (making it up). In other words, thermodynamic and informational entropies are rather compatible, which shouldn't be surprising since Claude Shannon derived the notation 'H' for information entropy from Boltzmann's H-theorem.
3. The capacity factor for thermal energy that is hidden with respect to temperature .
4. The dispersal of energy; how much energy is spread out in a process, or how widely spread out it becomes, at a specific temperature. 
2. () A measure of the amount of information and noise present in a signal.
3. (uncountable) The tendency of a system that is left to itself to descend into chaos.