{{For|conjugate variables in context of thermodynamics|Conjugate variables (thermodynamics)}}
In [[physics]], '''conjugateConjugate variables''' are pair of variables mathematically defined in such a way that they become [[Fourier transform]] [[dual (mathematics)|duals]] of one-another<ref>[http://www.aip.org/history/heisenberg/p08a.htm Heisenberg - Quantum Mechanics, 1925-1927: The Uncertainty Relations]</ref><ref>[http://www.eoht.info/page/Conjugate+variables Conjugate variables - Encyclopedia of Humanthermodynamics]</ref><ref>[http://www.springerlink.com/content/r40472577250313r/ Some remarks on time and energy as conjugate variables]</ref>, or more generally are related through [[Pontryagin duality]]<ref>[http://mathworld.wolfram.com/PontryaginDuality.html Pontryagin Duality -- from Wolfram MathWorld]</ref>. The duality relations lead naturally to an uncertainty (in [[physics]] called the [[Heisenberg uncertainty principle]]) relation between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty principle corresponds to the [[symplectic form]]<ref>[http://mathworld.wolfram.com/SymplecticForm.html Symplectic Form -- from Wolfram MathWorld]</ref>.
