Legendre transformation
In mathematics and physics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on the real-valued convex functions of one real variable. In physical problems, it is used to convert functions of one quantity (such as position, pressure, or temperature) into functions of the conjugate quantity (momentum, volume, and entropy, respectively). In this way, it is commonly used in classical mechanics to derive the Hamiltonian formalism out of the Lagrangian formalism and in thermodynamics to derive the thermodynamic potentials, as well as in the solution of differential equations of several variables.
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Adrien-Marie LegendreAnalytical mechanicsBRST quantizationCalculus of variationsCanonical coordinatesCanonical quantizationCanonical transformationChaplygin's equationChemical potentialChemical thermodynamicsClairaut's equation (mathematical analysis)Contact (mathematics)Contact geometryConvex conjugateCotangent bundleCramér's theorem (large deviations)Darwin LagrangianDe Donder–Weyl theoryDirac bracketDual curveDuality (mathematics)Effective actionF(R) gravityFenchel's duality theoremFiber derivativeFinite Legendre transformFree entropyFunctional renormalization groupGeometrothermodynamicsGibbs free energyGibbs–Duhem equationHamiltonian (control theory)Hamiltonian mechanicsHamiltonian opticsHeatHelmholtz free energyInformation field theoryIntegral of inverse functionsIntegration by partsIntensive and extensive properties
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Legendre transformation
In mathematics and physics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on the real-valued convex functions of one real variable. In physical problems, it is used to convert functions of one quantity (such as position, pressure, or temperature) into functions of the conjugate quantity (momentum, volume, and entropy, respectively). In this way, it is commonly used in classical mechanics to derive the Hamiltonian formalism out of the Lagrangian formalism and in thermodynamics to derive the thermodynamic potentials, as well as in the solution of differential equations of several variables.
has abstract
A transformada de Legendre con ...... mpre contidas na nova equação.
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En matemàtica es diu que dues ...... nom per Adrien-Marie Legendre.
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En matemáticas se dice que dos ...... ebido a Adrien-Marie Legendre.
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In analisi funzionale, il funz ...... dalla derivata dell'argomento.
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In de wiskunde is de legendret ...... ƒ* die wordt gedefinieerd door
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In mathematics and physics, th ...... ruct a function's convex hull.
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La transformation de Legendre ...... à l'hamiltonien et vice versa.
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Transformacja Legendre’a – prz ...... ka Adriena-Mariego Legendre’a.
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Перетворення Лежандра для зада ...... інійних функцій на просторі V.
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Преобразование Лежандра для за ...... функционалов на пространстве .
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A transformada de Legendre con ...... mpre contidas na nova equação.
@pt
En matemàtica es diu que dues ...... nom per Adrien-Marie Legendre.
@ca
En matemáticas se dice que dos ...... el requisito adicional de que
@es
In analisi funzionale, il funz ...... da trasformazioni di Legendre.
@it
In de wiskunde is de legendret ...... ƒ* die wordt gedefinieerd door
@nl
In mathematics and physics, th ...... quations of several variables.
@en
La transformation de Legendre ...... à l'hamiltonien et vice versa.
@fr
Transformacja Legendre’a – prz ...... ka Adriena-Mariego Legendre’a.
@pl
Перетворення Лежандра для зада ...... інійних функцій на просторі V.
@uk
Преобразование Лежандра для за ...... функционалов на пространстве .
@ru
label
Legendre transformation
@en
Legendre-Transformation
@de
Legendretransformatie
@nl
Transformacja Legendre’a
@pl
Transformada de Legendre
@ca
Transformada de Legendre
@es
Transformada de Legendre
@pt
Transformation de Legendre
@fr
Trasformata di Legendre
@it
Перетворення Лежандра
@uk