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The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy. To this approximation, then, 
where now the average is over the equilibrium ensemble and use has been made of the fact that the mean values of the αiare zero in equilibrium. Regarding Ji as a function of the Xi, one may write: 
with 
It is at this point that the principle of microscopic reversibility becomes relevant. If the dynamical equations of motion of the system are reversible in the time—as they will be if no magnetic field or Coriolis forces are present—then the cross-correlation function <α i(t + τ)aj(t)> between the displacements αi and αj must be symmetrical in τ. It follows directly that Lij = Lji, or, more generally, that in a magnetic field H: 
This set of equations is Onsager's famous Reciprocal Relations. Onsager first announced this result in 1929 (1929,1), but "in view of the very general claims I felt that concepts and conditions ought to be defined with great care, and a complete exposition did not appear until 1931." The claims were general indeed, and the Reciprocal Relations are now often referred to as the Fourth Law of Thermodynamics. Like the other equations of thermodynamics, they are at the same time mathematically simple and physically deep.
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