Everything about Onsager Reciprocal Relations totally explained
In
thermodynamics, the
Onsager reciprocal relations express the equality of certain relations between
flows and
forces in
thermodynamic systems out of
equilibrium, but where a notion of
local equilibrium exists.
As an example, it's observed that
temperature differences in a system lead to
heat flows from the warmer to the colder parts of the system. Similarly,
pressure differences will lead to
matter flow from high-pressure to low-pressure regions. It was observed
experimentally that when both pressure and temperature vary, pressure differences can cause heat flow and temperature differences can cause matter flow. Even more surprisingly, the heat flow per unit of pressure difference and the
density (matter) flow per unit of temperature difference are equal. This was shown to be necessary by
Lars Onsager using
statistical mechanics.
Similar "reciprocal relations" occur between different pairs of forces and flows in a variety of physical systems.
The theory developed by Onsager is much more general than this example and capable of treating more than two thermodynamic forces at once.
Example: Fluid system
Thermodynamic potentials, forces and flows
The basic
thermodynamic potential is internal
energy. In a
fluid system, the energy density
depends on matter density
and entropy density
in the following way:
»
where
is temperature and
is a combination of pressure and
chemical potential. We can write
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