Entropy

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.

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

<math> dS=\frac{dQ}{T} </math>

For a measurable change between two states i and f this expression integrates to

<math> \Delta S=\int_{i}^{f}\frac{dQ}{T} </math>

Statistical mechanics definition 1

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

<math> S= k_B \log W </math>

where <math>k_B</math> is Boltzmann's constant.

Statistical mechanics definition 2

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

<math> S=-k_B \sum_i^N p_i \log p_i </math>

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

See also

• History of the development of entropy