260 entropy. In a small paper with the microbiologist Jean- Marie Wiame, Prigogine discusses the possibility that also biological systems evolve towards states of minimal entropy production corresponding to minimal metabolism and suggests that this tendency leads to an increase in complexity during phylogenetic evolution (Prigogine and Wiame 1946). Although this was a fairly speculative idea, it illustrates the strong interest in biological questions which distinguished Prigogine from his fellow physicists who provided major contributions to non-equilibrium thermody- namics such as Carl Eckart, Josef Meixner and Lars Onsager. Thus, it is not surprising that even Prigogine’s early work on linear thermodynamic systems close to equilibrium was immediately discussed by biologists (Bertalanffy 1949; Spanner 1953). Between 1947 and 1967, Prigogine and co-workers in Brussels attempted to extend non-equilibrium thermody- namics to situations far from equilibrium. Initially, they focussed on hydrodynamic instabilities like the Rayleigh– Bérnard convection, which was experimentally very well described (Glansdorff and Prigogine 1971). In parallel, the first papers on chemical systems were published. A crucial question was whether the current formalism could be applied to periodic phenomena. The first two papers addressing this question were written using the Lotka– Volterra mechanism as a kinetic example, with the aim to show that oscillations do not in principle violate the laws of thermodynamics (Prigogine and Balescu 1956; Prigogine and Balescu 1958). Balescu recalls that speaking of chemical oscillations ‘was highly “politically incorrect” at that time’ (Balescu 2007, 12). In the discussion of his 1958 paper by leading specialists in the field, one of the participants remarks ‘…I should like the authors to ask if actual systems have been observed whose behaviour approaches that of the model, or is there somewhere a contradiction in the reaction scheme proposed which makes such behaviour impossible’ (Prigogine and Balescu 1958). However, in the following decade, the work of the Brussels school received increasing recognition. The term dissipative structure for states of coherent temporal or spatial order which are maintained far from equilibrium by the dissipa- tion of energy became a trademark (Prigogine 1969). A consensus view emerged of how chemical oscillations, chemical waves or stable spatial patterns in a homogeneous system were compatible with an extended thermodynamic formalism (Nicolis and Prigogine 1977). In brief, chemical oscillations cannot occur as deviations around a chemical equilibrium state like the mechanical oscillations of a pendulum. Nor can they occur close to equilibrium in a steady-state situation characterised by minimum entropy production as Prigogine pointed out already in his earliest writing on irreversible thermodynamics (Prigogine 1947). Rather, the periodic changes in concentration require a Dev Genes Evol (2011) 221:255–279 situation far from equilibrium, in which chemical reactions need not be reversible and detailed balancing does not apply. In a closed container without exchange of matter with the surrounding environment, reactions have to be postulated which produce substances to perpetuate the oscillations. The oscillations continue as long as sufficient amounts of these substances are provided and cease when they are consumed. Thus, the situation in the homogeneous phase is energetically similar to the example of the flame where the flux of matter clearly transgresses distinct phases. The flame arises and is maintained in a highly structured environment while dissipative structures represent the spontaneous formation of order from an unstructured starting situation. To develop a thermodynamic formalism which charac- terises the system behaviour far from equilibrium, Prigo- gine and his co-workers required chemical models for oscillating reactions or spatial patterning. The only existing model for chemical oscillations, the Lotka equations, turned out to be inappropriate for describing realistic situations (Nicolis and Portnow 1973). Chemical oscillations occur- ring in the laboratory should be characterised by a certain degree of structural stability, i.e. small variations in the starting concentrations should not affect the final oscillatory behaviour. Otherwise, it would be impossible to observe oscillations as a coherent behaviour of e.g. 1020 molecules in spite of naturally occurring fluctuations. However, exactly this feature of structural stability is lacking in the Lotka equations. They represent a conservative system more similar to the mathematical pendulum admitting an infinite number of different periodic solutions whose periods and amplitudes are fixed by the initial conditions. In search for a more realistic model for oscillations, the Brussels school could not work with any of the experimen- tally described cases. Neither the mechanism of the BZ reaction nor that of the Bray oscillator had been elucidated. The same applied for oscillations in biochemical systems which recently had been discovered (Ghosh and Chance 1964). In the absence of a model for oscillations, the Brussels school first investigated the Turing mechanism of spatial patterning, which, as we will see, was entirely based on biological reasoning (Prigogine and Nicolis 1967; Turing 1952). However, soon they presented a theoretical example of an oscillator which showed structural stability (limit cycle oscillations, Prigogine and Lefever 1968). It became subject of a large body of theoretical work and was later dubbed the Brusselator (Tyson 1973). In comparison to the Lotka mechanism, structurally stable limit cycle oscillations require at least three reactions, cross catalysis and non-linear autocatalysis; in the case of two-component systems (like the Brusselator), the autocatalytic reaction has to be trimolecular (Nicolis and Portnow 1973; Schnakenberg 1979). Prigogine and Lefever (1968) mention that ‘this