Irreversibility and Emergence in Nonequilibrium Systems
From COSNet
Most systems in nature are in nonequilibrium states, and over the years considerable effort has been devoted to the development of nonequilibrium statistical mechanics and nonequilibrium thermodynamics. By applying these concepts and methodologies we can probe the fundamental issues at the very roots of complexity and thus extend insights gained for one set of complex physical systems to other complex systems.
In general, systems in nature are in non-equilibrium states, and the accompanying fluxes of matter, energy, etc. are irreversible. The second law of thermodynamics fixes the direction of these irreversible processes by specifying that the accompanying entropy production is always positive. This is so regardless of whether the system is open or closed, and independently of whether entropy flows into or out of the system to its surroundings. For the special case of an isolated system, the second law thus indicates that entropy can never decrease, but it is important to note that for open systems entropy can either increase or decrease. That is, the sign of entropy change of a system is generally NOT specified by the second law. The matter is discussed in text books on the subject (e.g. de Groot and Mazur). The implications are both profound and far-reaching:
1) Since most systems are not isolated: they are open in various ways, being subject to mass, energy, entropy, (and, more abstractly, information fluxes across their boundaries). Although the total entropy of a system plus its environment (which together constitute an isolated system) must increase, we emphasise again that it does not follow that the entropy of an open system must increase. Instead, there are many remarkable instances of self-organization of such systems into coherent structures, ranging from tropical cyclones through individual biological organisms to human civilizations -- are there general principles to determine when self-organization will occur? This is a question which arises independently of the second law.
2) It is well known that the equilibrium state of a system may be determined by applying a variational principle, eg, maximising entropy for an isolated system, or minimising Helholtz free energy for a system in contact with a thermal reservoir. On the other hand, for non-equilibrium systems, variational principles apply not to entropy per se, but to rather to entropy production [1,2,3]. The development of extremal principles for complex systems will be an important goal in our program.
3) Thermodynamics applies in the limit of very large numbers of interacting entities -- in finite systems how important are fluctuations temporarily violating the second law?
In NE systems, irreversible behaviour occurs as information is lost in the observation process, even though the microscopic equations are reversible. Driving a system away from equilibrium produces symmetry breaking and consequent emergence of organization but can also produce turbulence if the forcing is too strong. Questions related to the statistical thermodynamics of irreversibility and self-organization are important in a wide range of new and cross-disciplinary fields, such as evolutionary dynamics, artificial life, self assembly, phase separation, and turbulence.
NESM has been extensively tested only on idealized complex systems, whereas it is hoped that principles such as Maximimum Entropy Production (MEP) can be more easily applied to a wide variety of complex systems. Links between the rigorous theory of NESM and the hypothesis of MEP have already been made. One approach [2] is based on information theory and dictates that the Shannon information entropy is maximized, subject to some constraints. The Shannon information entropy expresses entropy in terms of the probability distribution of observations, or the information contained in a set of observations. However, there are various issues that are currently being explored including: clarification of the definition of entropy from a microscopic perspective; the influence of the constraints on the MEP results; and algorithms for maximizing the entropy production.
Surprises occur even in physical systems as seemingly well-known as the mixing of water and methanol [4], where the entropy increase is reduced by self-organization. While Australia has a strong NESM tradition in chemical physics, information and entropy concepts are becoming increasingly important in diverse fields. For instance, Parunak and Brueckner [5] in the context of pheromone-based coordination define a way to measure entropy at the macro level (ant-like agents' behaviours lead to orderly spatiotemporal patterns) and micro level (chaotic diffusion of pheromone molecules) in such a way that the overall information entropy increases, consistently with the second law of thermodynamics even though this is not a physical system in the usual sense.
[1] I Prigogine, Thermodynamics of Irreversible Processes (1961 New York: Interscience)
[2] M. Ichiyanagi, Phys Rep 243, 125-82 (1994)
[3] R (not RL) Dewar, Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states, J. Phys. A: Math. Gen. 36, 631 (2003)
[4] J.-H. Guo et al, Molecular Structure of Alcohol-Water Mixtures, Phys. Rev. Letters 91, 157401-1 (2003)
[5] H. Van Dyke Parunak and Sven Brueckner. Entropy and self-organization in multi-agent systems. In Proceedings of the 5th International Conference on Autonomous agents, Montreal, Canada, 2001.
*As Parunak and Brueckner [5] remark: 'While we are not prepared at this point to define the precise correspondence between ergs and bits, we believe that physical models are an under-exploited resource for understanding computational systems in general and multi-agent systems in particular. The fact that the thermodynamic and information approaches work in different fundamental units (ergs vs. bits) is not a reason to separate them, but a pole star to guide research that may ultimately bring them together.'
