Fundamental conceptual problems that arise from the macroscopic and microscopic aspects of the second law of thermodynamics are considered. It is shown that nonequilibrium may become a source of order and that irreversible processes may lead to a new type of dynamic states of matter called "dissipative structures." The thermodynamic theory of such structures is outlined. A microscopic definition of irreversible processes is given, and a transformation theory is developed that allows one to introduce nonunitary equations of motion that explicitly display irreversibility and approach to thermodynamic equilibrium. The work of the group at the University of Brussels in these fields is briefly reviewed. In this new development of theoretical chemistry and physics, it is likely that thermodynamic concepts will play an ever-increasing role.

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Time, structure, and fluctuations.

We have seen that the formation and maintenance of self‐organizing systems are compatible with the laws of physical chemistry. We must now confront this idea with the major problem of biology: How did biological systems arise?

Thermodynamics of evolution

Visual information processing in the nervous system of flies begins with a large array of photoreceptors, which transduce a light intensity pattern, and culminates in a behavioural response that depends on that pattern.In the previous paper we have given a quantitative description of visual control of flight orientation in the fly. This description can account for fixation, tracking and some instances of spontaneous pattern preference behaviour. The phenomenological theory outlines the basic logical organization of the visual control system of the fly. It requires the neural network between the receptors and the flight muscles to perform two main computations on the visual input. One computation extracts movement information (the term r(ψ)ψ b of the phenomenological equation). The other provides position information (the term D(ψ)).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0033583500002535

Visual control of orientation behaviour in the fly: Part II. Towards the underlying neural interactions

A fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation. The theorem is expressed in terms of the generating and large-deviation functions characterizing the fluctuations of a quantity which measures the loss of detailed balance out of thermodynamic equilibrium. The relationship to entropy production is established and discussed. The fluctuation theorem is verified in the Schlogl model of far-from-equilibrium bistability.

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Fluctuation theorem for nonequilibrium reactions

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution.

/pdf/fluctuation-theorem-for-currents-and-schnakenberg-network-37ui8pvrqa.pdf

Fluctuation Theorem for Currents and Schnakenberg Network Theory

The theory of fluctuations is extended to nonlinear systems far from equilibrium. Systems whose evolution involves two separate time scales, e.g., chemically reacting mixtures near a local equilibrium regime, are studied in detail. It is shown that the usual stochastic description of chemical kinetics based on a “birth and death” model is inadequate and has to be replaced by a more detailed phase-space description. This enables one to develop for such systems a plausible mechanism for the emergence of instabilities, in which the departure from the steady state is governed by large fluctuations of macroscopic size, while small thermal fluctuations are still described by a generalization of Einstein's equilibrium theory. On the other hand, far from a local equilibrium regime, infinitesimal fluctuations may increase and attain macroscopic values. In this case the system evolves to a state of “generalized turbulence”, in which the distinction between macroscopic averages and fluctuations becomes meaningless.

https://www.pnas.org/content/pnas/68/9/2102.full.pdf

I. Prigogine

Papers

Fluctuations in Nonequilibrium Systems