Legendre transformation

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"Legendre Transformation Consider a function of two variables f (x, y so that df = udx + vdy u= ∂f ∂x v= y ∂f ∂y x Now we wish to change the variables (x, y) → (u, y). To that aim we introduce g = f − ux The differential of g dg = df − udx − xdu = udx + vdy − udx − xdu = vdy − xdu The quantities x and v are now the functions of the variables u and y defined by x=− ∂g ∂u v= y (1) ∂g ∂y u 1 ..."

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