: Matemáticas: Legendre transformation

mathematical physics > Legendre transformation

geometry > convex analysis > Legendre transformation

mathematical analysis > real analysis > real-valued function > function of several real variables > Legendre transformation

Legendre transformation

In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions of one quantity (such as velocity, 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 (or vice versa) and in thermodynamics to derive the thermodynamic potentials, as well as in the solution of differential equations of several variables.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Legendre_transformation)

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