These quantities are defined in the article on Onsager reciprocal relations.

The Onsager reciprocal relations are sometimes called the fourth law of thermodynamics.

This fact is called the Onsager reciprocal relations.

The tensor is symmetric by the Onsager reciprocal relations.

These symmetry relations, , are exactly the Onsager reciprocal relations.

The Onsager reciprocal relations in particular, are developed in terms of entropic potentials.

Except in special cases, this matrix is symmetric as expressed in the Onsager reciprocal relations.

The matrix of the kinetic coefficients should be symmetric (Onsager reciprocal relations) and positive definite (for the entropy growth).

As the fourth law of thermodynamics Onsager reciprocal relations would constitute the fourth principle of energetics.

In the field of near-equilibrium thermodynamics, the Onsager reciprocal relations and the Green-Kubo relations fall out very directly.

Such conjugate pairs are particularly useful in the analysis of irreversible processes, as exemplified in the derivation of the Onsager reciprocal relations.

The article on Onsager reciprocal relations considers the stable near-steady thermodynamically non-equilibrium regime, which has dynamics linear in the forces and flux densities.

In physics and chemistry, there are two main macroscopic consequences of the time-reversibility of microscopic dynamics: the principle of detailed balance and the Onsager reciprocal relations.

In physical and chemical kinetics, T-symmetry of the mechanical microscopic equations implies two important laws: the principle of detailed balance and the Onsager reciprocal relations.

These symmetry relations were proved on the basis of the time reversibility of microscopic dynamics (Microscopic reversibility) as Onsager reciprocal relations.

The most commonly proposed Fourth Law is the Onsager reciprocal relations, which give a quantitative relation between the parameters of a system in which heat and matter are simultaneously flowing.

The fourth law of thermodynamics is not yet an agreed upon law (many supposed variations exist); historically, however, the Onsager reciprocal relations have been frequently referred to as the fourth law.

In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists.

Keizer used the canonical form for the first formulation of statistical thermodynamics valid in far from equilibrium regimes, where the Onsager reciprocal relations and the Einstein formula for the fluctuations do not work.

His research at Brown was concerned mainly with the effects on diffusion of temperature gradients, and produced the Onsager reciprocal relations, a set of equations published in 1929 and, in an expanded form, in 1931, in statistical mechanics whose importance went unrecognized for many years.

He explains that the Onsager reciprocal relations concern variables which are even functions of the velocities of the molecules, and notes that Casimir went on to derive anti-symmetric relations concerning variables which are odd functions of the velocities of the molecules.

Experimental verifications of the Onsager reciprocal relations were collected and analyzed by D.G. Miller for many classes of irreversible processes, namely for thermoelectricity, electrokinetics, transference in electrolytic solutions, diffusion, conduction of heat and electricity in anisotropic solids, thermomagnetism and galvanomagnetism.