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

$dS={\frac {dQ}{T}}$

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

$\Delta S=\int _{i}^{f}{\frac {dQ}{T}}$

Statistical mechanics definition 1

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

$S=k_{B}\log W$

where $k_{B}$ 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 $p_{i}$, 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.

See also

• History of the development of entropy