Conjugate variables: Difference between revisions

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Revision as of 15:43, 16 March 2008

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{{for|conjugate variables in context of thermodynamics|Conjugate variables (thermodynamics)}}

==Thermodynamics==

*[[Conjugate variables (thermodynamics)]] - the expression of all [[thermodynamic potential]]s are expressed in terms of conjugate pairs.

==Physics==

In [[physics]], '''conjugate variables''' are pair of variables mathematically defined in such a way that they become [[Fourier transform]] [[dual (mathematics)|duals]] of one-another, or more generally are related through [[Pontryagin duality]]. The duality relations lead naturally to an uncertainty ([[Heisenberg uncertainty principle]]) relation between them.

A more precise [[mathematical]] definition, in the context of [[Hamiltonian mechanics]], is given in the article [[canonical coordinates]].

===Examples===

Examples of canonically conjugate variables include the following:

* [[Time]] and [[frequency]]: the longer a musical note is sustained, the more precisely we know its frequency (but it spans more time). Conversely, a very short musical note becomes just a click, and so one can't know its frequency very accurately.