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==Thermodynamics==
A pair of variables mathematically defined in such a way that they become [[Fourier transform]] 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. ▼
*[[Conjugate variables (thermodynamics)]] - the expression of all [[thermodynamic potential]]s are expressed in terms of conjugate pairs.
==Physics==
▲A pair of variables mathematically defined in such a way that they become [[Fourier transform]] 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 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.
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