Dissipative structures

A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter.

A dissipative structure, term coined by Ilya Prigogine, Nobel prize of Chemistry in 1977, is a dissipative system that has a dynamical régime that is in some sense in a reproducible steady state. This reproducible steady state may be reached by natural evolution of the system, by artifice, or by a combination of these two. Put simply, something dissipative if it loses energy to waste-heat or not technically, if volume in the phase space is not conserved. The famous Second Law of Thermodynamics amounts to saying that, if something is isolated from the rest of the world, it will dissipate all the free energy it has. Equivalently, it maximizes its entropy. Thermal equilibrium is the state of maximum entropy. Near thermal equilibrium, the behavior of the system is governed by linear differential equations (hence the name “linear thermodynamics”), and that left to itself it will approach equilibrium exponentially (hence the somewhat more common name “irreversible thermodynamics”). Here we are guided, not by the entropy, but by “entropy production,” the rate of increase in entropy. Since, once we reach equilibrium, the entropy cannot increase (by definition), the entropy production at equilibrium is zero, and the entropy production is always decreasing (the “principle of minimum entropy production”).

Critics say that, however hings are not well-isolated from the rest of the world. If energy arrives from the outside as quickly as it is dissipated, even bodies in the linear regime can be kept away from equilibrium. So you can have structures in dissipative systems, and there’s no reason not to call them “dissipative structures”, though it’s not obvious that there are many interesting generalizations about them.

“Far-from-equilibrium” means that your system is so far from its thermal equilibrium that the linear laws I mentioned a moment ago no longer apply; non-linear terms become important. The only general rule about the solution to non-linear differential equations is that there are no general rules; hence the interest in the subject. (Cf. Chaos and non-linear dynamics.) This is not good news, of course, if what you want to do is extend thermodynamics to the far-from-equilibrium case. But, one might suppose, matters are not totally hopeless; we aren’t talking about just any arbitrary system of equations, but the particular ones important in thermodynamics; perhaps there is some general principle (like those of maximum entropy, or minimum entropy production) which can guide us to solutions.

See also

Nonequilibrium Statistical Mechanics, Self-organization, Irreversible Thermodynamics

Papers

• Kugler, P. N., Kelso, J. S., & Turvey, M. T. (1980). On the concept of coordinative structures as dissipative structures: I. Theoretical lines of convergence. Tutorials in motor behavior, 3, 3-47.

Books

• Kondepudi, D., & Prigogine, I. (2014). Modern thermodynamics: from heat engines to dissipative structures. John Wiley & Sons.
• Kubicek, M., & Marek, M. (2012). Computational methods in bifurcation theory and dissipative structures. Springer Science & Business Media.