Bifurcation

Bifurcation (pitchfork)
Diagram of a pitchfork bifurcation, in which concentration X is a function of parameter λ, which measures the distance from equilibrium, whereby at the bifurcation point, the thermodynamic branch becomes unstable, and the two new solutions b1 and b2 emerge. [1]
In thermodynamics, a bifurcation or “bifurcation point” refers to the splitting of a thermodynamic branch, some distance from equilibrium, into two new branches.

History
The term "bifurcation" seems to have originated in Henri Bergson's 1907 chapter "The Divergent Directions of the Evolution of Life", in his book Creative Evolution, where he states that "nature preserves the different tendencies that have bifurcated with their growth, creating them with diverging series of species that will evolve separately."

This book was most influential to Belgian chemist Ilya Prigogine, who worked for many decades to explain Bergson's views thermodynamically.

The term ‘bifurcation’ is closely related to the term ‘fluctuation’, which are both largely conceptions of the work of Prigogine who defines bifurcation as the branching of a solution into multiple solutions as a system parameter is varied. [1]

Determinism
The main interest of Prigogine in advancing the thesis that humans are far from equilibrium types of evolved dissipative structures that are changed into new structures past bifurcation points is that it allowed for Prigogine to argue against complete determinism, to the effect that, in his view, the reaction and choice of the chemical entity is determined while in the thermodynamic branch, prior to the bifurcation point, but that at the point of bifurcation new choices emerge and the path become indeterminate.

References
1. Prigogine, Ilya. (1996). The End of Certainty: Time, Chaos, and the New Laws of Nature (glossary: bifurcation, pg. 201; pitchfork bifurcation diagram, pg. 69). Free Press.

Further reading
● Perrot, Pierre. (1998). A to Z of Thermodynamics (bifurcation, pgs. 18-19). Oxford University Press.
● Conte, Joseph M. (2002). Design and Debris: A Chaotics of Postmodern American Fiction (ch. 6: The Perfect Game: Dynamic Equilibrium and the Bifurcation Point in Robert Coover’s The Universal Baseball Association, pgs. 140-62). University of Alabama Press.

Videos
● Prigogine, Ilya. (2008). “On Art and Bifurcations” (Ѻ), formulador, Mar 4.

External links
Bifurcation – Wikipedia.

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