Second law evolution problem
In outlining what they define as "the problem", i.e. the issue of the tendency towards disorder in the second law verses the tendency towards order in evolution, they state:
“Coherent behavior is the characteristic feature of biological systems (ordered structures), reflective of structures acquired during long periods of evolution.”
In contrast, according to the second law, they point out that:
“The evolution of a physicochemical system leads to an equilibrium state of maximum disorder.”
They then note that this last statement holds for isolated systems; albeit they neglect to mention that this only holds for systems that obey the Boltzmann chaos assumption, i.e. ideal gas phase systems. In continuation with their chain of logic, the state that for a system in contact with an energy reservoir at a temperature T, its state is defined by the following function of free energy, F, where:
F = E – TS
where E is the internal energy, and S is the entropy of the system; a function defined such that at equilibrium F is a minimum. The then state that at low temperatures, according to this function, ordered low-entropy structures, such as crystals, can appear. In admonition, however, they state:
“Unfortunately this principle cannot explain the formation of biological structures.”
Curiously, to note, in laying out this argument they choose to utilize Helmholtz free energy (constant volume processes) rather than Gibbs free energy (constant pressure processes), which can explain the formation of biological structures. It is likely that Prigogine chooses his presentation in this manner so as to not effect a weakening in his later arguments; in the sense that he wants to discredit any detail not in alignment with his view that nonequilibrium thermodynamics is the key to explain biological evolution.
In any event, they then explain that their supposition is true because, as they reason, the probability that a macroscopic number of molecules will assemble to form higher ordered living structures is “vanishingly small” at ordinary temperatures. This argument, however, traces to the intersection of the 1890 Poincaré recurrence theorem, which states that, given a long enough time, there exists a small probability that an isolated dynamical system can return to its initial state (ordered); which conflicts with the second law which states that such a system will continue to move towards a more disordered final state. In any event, curiously, Prigogine repeates this same argument in the opening words of his 1977 Nobel Lecture “Time, Structure and Fluctuations.”  They then conclude:
“The apparent contradiction between biological order and the laws of physics—in particular the second law of thermodynamics—cannot be resolved as long as we try to understand living systems by the methods of familiar equilibrium statistical mechanics and equally familiar thermodynamics.”
To solve this issue, in their article, on the lead of Prigogine, the introduce the Prigoginean thermodynamics logic of nonequilibrium open systems, internal entropy, dissipative structures, order through fluctuations, feedback, among other factors.
1. (a) Prigogine, Ilya, Nicolis, Gregoire, and Babloyants, Agnes. (1972). "Thermodynamics of Evolution," (part I). Physics Today (pgs. 23-28), Vol. 25, November.
(b) Prigogine, Ilya, Nicolis, Gregoire, and Babloyants, Agnes. (1972). "Thermodynamics of Evolution," (part II). Physics Today (pgs. 38-44), Vol. 25, December.
2. Prigogine, Ilya. (1977). “Time, Structure and Fluctuations”, Nobel Lecture, Dec. 08.