The Onsager Relations
Following Section III of Rayleigh (1873), Onsager (1931, I) showed that in the regime where both the flows are small and the thermodynamic forces vary slowly, there will be a linear relation between them, parametrized by a matrix of coefficients conventionally denoted :
The second law of thermodynamics requires that the matrix be positive definite. Statistical mechanics considerations involving microscopic reversibility of dynamics imply that the matrix is symmetric. This fact is called the Onsager reciprocal relations.
Read more about this topic: Non-equilibrium Thermodynamics
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“Children, who play life, discern its true law and relations more clearly than men, who fail to live it worthily, but who think that they are wiser by experience, that is, by failure.”
—Henry David Thoreau (1817–1862)