Energy dissipation and entropy production extremal principles are ideas developed within non-equilibrium thermodynamics that attempt to predict the likely steady states and dynamical structures that a physical system might show.
[1][2][3][4][5][6] According to Kondepudi (2008),[7] and to Grandy (2008),[8] there is no general rule that provides an extremum principle that governs the evolution of a far-from-equilibrium system to a steady state.
Lebon Jou and Casas-Vásquez (2008)[10] state that "In non-equilibrium ... it is generally not possible to construct thermodynamic potentials depending on the whole set of variables".
Šilhavý (1997)[11] offers the opinion that "... the extremum principles of thermodynamics ... do not have any counterpart for [non-equilibrium] steady states (despite many claims in the literature)."
Apparent 'fluctuations', which appear to arise when initial conditions are inexactly specified, are the drivers of the formation of non-equilibrium dynamical structures.
These inexactitudes of specification are the source of the apparent fluctuations that drive the generation of dynamical structure, of the very precise but still less than perfect reproducibility of non-equilibrium experiments, and of the place of entropy in thermodynamics.
The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result.
[20][21] According to this view of Jaynes, it is a common and confusing abuse of language, that one often sees reproducibility of dynamical structure called "order".
According to Glansdorff and Prigogine (1971, page 15),[9] in general, these principles apply only to systems that can be described by thermodynamical variables, in which dissipative processes dominate by excluding large deviations from statistical equilibrium.
This means that collisions between molecules are so frequent that chemical and radiative processes do not disrupt the local Maxwell-Boltzmann distribution of molecular velocities.
Autocatalytic reactions provide examples of non-linear dynamics, and may lead to the natural evolution of self-organized dissipative structures.
This arises from the momentum of the fluid flow, showing a different kind of dynamical structure from that of the conduction of heat or electricity.
The definition of the rate of entropy production of such a flow is not covered by the usual theory of classical non-equilibrium thermodynamics.
There are many other commonly observed discontinuities of fluid flow that also lie beyond the scope of the classical theory of non-equilibrium thermodynamics, such as: bubbles in boiling liquids and in effervescent drinks; also protected towers of deep tropical convection (Riehl, Malkus 1958[30]), also called penetrative convection (Lindzen 1977[31]).
When heat is created by any unreversible process (such as friction), there is a dissipation of mechanical energy, and a full restoration of it to its primitive condition is impossible.
When radiant heat or light is absorbed, otherwise than in vegetation, or in a chemical reaction, there is a dissipation of mechanical energy, and perfect restoration is impossible."
"[36] In 1878, Helmholtz,[37] like Thomson also citing Carnot and Clausius, wrote about electric current in an electrolyte solution with a concentration gradient.
Studying jets of water from a nozzle, Rayleigh (1878,[27] 1896/1926[28]) noted that when a jet is in a state of conditionally stable dynamical structure, the mode of fluctuation most likely to grow to its full extent and lead to another state of conditionally stable dynamical structure is the one with the fastest growth rate.
Prigogine was present when this paper was read and he is reported by the journal editor to have given "notice that he doubted the validity of part of Ziman's thermodynamic interpretation".
The physics of the earth's atmosphere includes dramatic events like lightning and the effects of volcanic eruptions, with discontinuities of motion such as noted by Helmholtz (1868).
Jou, Casas-Vazquez, Lebon (1993)[57] note that classical non-equilibrium thermodynamics "has seen an extraordinary expansion since the second world war", and they refer to the Nobel prizes for work in the field awarded to Lars Onsager and Ilya Prigogine.
Martyushev and Seleznev (2006)[4] note the importance of entropy in the evolution of natural dynamical structures: "Great contribution has been done in this respect by two scientists, namely Clausius, ... , and Prigogine."
Glansdorff and Prigogine (1971)[9] wrote on page xx: "Such 'symmetry breaking instabilities' are of special interest as they lead to a spontaneous 'self-organization' of the system both from the point of view of its space order and its function."
Šilhavý (1997)[11] offers the opinion that "... the extremum principles of [equilibrium] thermodynamics ... do not have any counterpart for [non-equilibrium] steady states (despite many claims in the literature)."
[62] A proposal closely related to Prigogine's is that the pointwise rate of entropy production should have its maximum value minimized at the steady state.
[65][66] Onsager (1931, I)[1] wrote: "Thus the vector field J of the heat flow is described by the condition that the rate of increase of entropy, less the dissipation function, be a maximum."
He demonstrated his principle using vector space geometry based on an “orthogonality condition” which only worked in systems where the velocities were defined as a single vector or tensor, and thus, as he wrote[3] at p. 347, was “impossible to test by means of macroscopic mechanical models”, and was, as he pointed out, invalid in “compound systems where several elementary processes take place simultaneously”.
In relation to the earth's atmospheric energy transport process, according to Tuck (2008),[49] "On the macroscopic level, the way has been pioneered by a meteorologist (Paltridge 1975,[50] 2001[69])."
[69] Sawada (1981),[71] also in relation to the Earth's atmospheric energy transport process, postulating a principle of largest amount of entropy increment per unit time, cites work in fluid mechanics by Malkus and Veronis (1958)[72] as having "proven a principle of maximum heat current, which in turn is a maximum entropy production for a given boundary condition", but this inference is not logically valid.
C. Nicolis (1999)[74] concludes that one model of atmospheric dynamics has an attractor which is not a regime of maximum or minimum dissipation; she says this seems to rule out the existence of a global organizing principle, and comments that this is to some extent disappointing; she also points to the difficulty of finding a thermodynamically consistent form of entropy production.