Entropy is an information theoretical concept applied across physics, information theory, mathematics and other branches of science and engineering. When given a system whose exact description is not precisely known, the entropy is defined as the expected amount of information needed to exactly specify the state of the system, given what we know about the system. The entropy (S) can be computed using the following formula:[3]
Here the summation is over the possible precisely defined states i the system can be in, and the Pi are the probabilities for the system to be in these states, given what we know about the system. The constant of proportionality k depends on what units are chosen to measure S. To measure the entropy in terms of bits the logarithm may be written in base 2.[4] When the above expression is written in base 2 the constant k is multipled by ln(2).[5]
In thermodynamics, the entropy is intimately related to the internal energy of the system. Given that there are a large number of molecules in the system, there are a huge number Ω of quantum states available to the system. Boltzmann gave arguments in favor of the hypothesis that for an isolated system, the probability distribution over the set of available states is a uniform distribution in thermal equilibrium. Assuming this hypothesis, we can write
- .
The standard choice for the constant k in thermodynamics is the Boltzmann constant kB = 1.38066×10−23 J K−1.
Entropy is central to the second law of thermodynamics. The second law in conjunction with the fundamental thermodynamic relation places limits on a system's ability to do useful work.[6][7]
The second law can also be used to predict whether a physical process will proceed spontaneously. Spontaneous changes in isolated systems occur along with an increase in entropy.
The word "entropy" is derived from the Greek εντροπία "a turning toward" (εν- "in" + τροπή "a turning").[8]
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New York Times
Every bit as striking as Ballard's feeling for entropy is his engagement with arts from which literature too often seems quarantined: music, sculpture, ...
