Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 5.2-2

THE EXTREMUM PRINCIPLE IN THE LEGENDRE TRANSFORMED REPRESENTATIONS

Physics — Statistical Mechanics · legendre-transform-exponential

Problem

Let

y = Ae^{Bx}

a

) Find

\psi(P)

b

) Calculate the inverse Legendre transform of

\psi(P)

and corroborate that this result is

y(x)

c

) Taking

A = 2

and

B = 0.5

, draw a family of tangent lines in accordance with the result found in (

a

), and check that the tangent curve goes through the expected points at

x = 0

, 1, and 2.