Entropy

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Entropy is a measure of disorder or information content in a system, first postulated by Lazare Carnot in 1803.

The second law of thermodynamics states that entropy will always increase over time within a closed system, defining a closed system as one in which neither matter nor energy may enter or leave.

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Definitions

Thermodynamic definition

In classical thermodynamics, if a small amount of energy dQ is supplied to a system from a reservoir held at temperature T, the change in entropy is given by


dS=\frac{dQ}{T}

Statistical mechanics definition 1

If a system can be arranged in W different ways, the entropy is

S = kBlogW

where kB is Boltzmann's constant.

Statistical mechanics definition 2

Label the different states a thermodynamic system can be in by i=1,2,3\ldots N. If the probability of finding the system in state i is pi, the entropy is


S=-k_B \sum_i^N p_i \log p_i

This definition is closely related to ideas in information theory, where the definition of information content is very similar to the definition of entropy.

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References

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