Should entropy and temperature be dual?
In Classical Continuum Mechanics, the entropy(s) and temperature(T) are considered to be dual in the second thermodynamics principle,
by define a relation between internal energy(e) and Helmhotz free energy(ψ): ψ = e - s * T . As you can find it in many CM books, such as [2008][J.N.Reddy]Introduction to Continuum Mechanics.
Here is my questions:
1. Is the transformation between internal energy and Helmhotz free energy a Legendre Transform?