Thermodynamics - Materials Science for Structural Geology - page 28

macroscopic theory adequately supported by experimental observation (Miller 1974 ).
Curie's principle concerning the symmetry relationships between cause and effect
(Curie 1894 ; Paterson and Weiss 1961 ) is also often invoked to constrain further the
possible values of L ab ; this principle being paraphrased to state that no direct coupling
occurs between processes described respectively by quantities of odd and even
tensorial character, for example, between chemical reaction (scalar) and diffusion
(vector). Then, we can put L ab ¼ 0 where a ; ba 6¼ ð Þ refer to two such processes,
although this does not prevent indirect interference occurring (Prigogine 1967 ,
p. 89). Other possible constraints on the L ab are discussed by Fisher and Lasaga 1981 .
One can expect non-equilibrium thermodynamics to be concerned also with the
likely paths to be followed by processes, with the nature of stationary states, and with
questions of stability, in analogy with topics in equilibrium thermodynamics such as
the criteria of equilibrium and conditions governing phase transitions. Actually,
when not ignored, these non-equilibrium topics appear to be the subject of consid-
erable debate and research, and only a few general remarks are appropriate here (for a
summary on stability considerations, see Prigogine 1980 ). It seems that a general
principle of fundamental and far-reaching importance is the principle of least dis-
sipation of energy (Lavenda 1978 , Chap. 6 ; Onsager 1931a , b ). In the particular case
of linear phenomenological laws, it follows that a system will evolve in the direction
of diminishing rate of entropy production, towards a state characterized by a mini-
mum rate of entropy production (Prigogine 1967 ). However, in a completely
unconstrained situation this minimum rate will be zero, reached when all irreversible
processes have stopped and equilibrium is attained. In order to maintain a stationary
or steady non-equilibrium state, that is, one that no longer evolves with time, it is
therefore necessary to constrain at least one term in the dissipation function Tr to be
nonzero, that is, to hold at least one of the thermodynamic forces X a at a constant,
nonzero value. It follows that in the stationary state all unconstrained parameters X a ;
J a will become zero. Thus the stationary state in any system in which linear processes
are occurring is that in which the rate of entropy production is a minimum under
certain auxiliary conditions such as specified nonzero values for at least one of the X a
or J a ; and this state will be stable.
For corresponding considerations in nonlinear and far from-equilibrium situations,
including the occurrence of stable ''dissipative'' structures, see (Glandsdorff and Prigogine
1971 ; Lavenda 1978 ; Prigogine 1980 ; Fisher and Lasaga 1981 and Ross 2008 ).

References

Callen HB (1960) Thermodynamics: an introduction to the physical theories of equilibrium
thermostatics and irreversible thermodynamics. Wiley, New York 376 pp
Callen HB (1974) A symmetry interpretation of thermodynamics. In: ed, Foundations of
continuum mechanics, London, Macmillan, pp 51-78; also in: foundation of physics 54
pp 423-443 (1974)