A classic Onsager reciprocity relation for Fourier heat conduction in the absence of magnetic fields states that the thermal conductivity tensor in. 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. "Reciprocal relations" occur between different pairs of forces and flows in a variety of physical systems.Example: Fluid system · The Onsager reciprocal · Abstract formulation. Both the FDT and Onsager's reciprocity relations rely on the assumption that macroscopic response and decay process occur in the same manner as the decay of equilibrium fluctuations - this assumption is called Onsager's regression hypothesis.
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Onsager reciprocity relation, since Fourier's law fails in thin dielectric films due to ballistic phonon transport effects, it is natural to ask whether an analogous Onsager relation can be identified in the boundary scattering regime.
To answer this question, we solve the Boltzmann onsager reciprocity relation equation BTE under the relaxation time approximation for in-plane and cross-plane heat transport for thin films with anisotropic phonon dispersion relations and scattering rates.
What is remarkable is the observation that, when both pressure and temperature vary, temperature differences at constant pressure can cause matter flow as in convection and pressure differences onsager reciprocity relation constant temperature can cause heat flow.
Perhaps surprisingly, the heat flow per unit of pressure difference and the density matter flow per unit of temperature difference are equal.
This equality was shown to be necessary by Lars Onsager using statistical mechanics as a consequence of the onsager reciprocity relation reversibility of microscopic dynamics microscopic reversibility.
The theory developed by Onsager is much more general than this example and capable of treating more than two thermodynamic forces at onsager reciprocity relation, with the limitation that "the principle of dynamical reversibility does not apply when external magnetic fields or Coriolis forces are present", in which case "the reciprocal relations break down".
In fact, Onsager's paper  refers to thermoelectricity and transport phenomena in electrolytes as well-known from the 19th century, including "quasi-thermodynamic" theories by Thomson and Helmholtz respectively.
In equilibrium, the entropy reaches a maximum. Onsager's reciprocal onsager reciprocity relation state the identities of the cross coefficients 3.
Onsager reciprocal relations - Wikipedia
The cross coefficients are a measure for the coupling of the single transport phenomena within onsager reciprocity relation system. A system with consists of independent irreversible processes, where every driving force only affects its connected flux.
A convenient form to identify the according affinities to given fluxes is obtained by considering the time derivative of the entropy 3.