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Concept
Maxwell relations
Summary
Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell.
Equations
symmetry of second derivatives
The structure of Maxwell relations is a statement of equality among the second derivatives for continuous functions. It follows directly from the fact that the order of differentiation of an analytic function of two variables is irrelevant (Schwarz theorem). In the case of Maxwell relations the function considered is a thermodynamic potential and x_i and x_j are two different natural variables for that potential, we have
where the partial derivatives are taken with all other natural variables held constant. For every thermodynamic potential there are \frac{1}{2} n(n-1) possible Maxwell relations where n i
Official source
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