Boltzmann brain fluctuation diagram, used in discussions of the Boltzmann brain problem.
In thermodynamics, a fluctuation refers to the cyclical deviation of some parameter above or below the mean.

The term "fluctuation" is difficult to give a precise meaning to and is significantly intertwined with Belgian chemist Ilya Prigogine’s theory of far-from-equilibrium dissipative structures and bifurcation points, as the following summary quote indicates: [1]

“All systems contain subsystems, which are continually ‘fluctuating’. At times, a single fluctuation or a combination of them may become so powerful, as a result of feedback, that it shatters the preexisting organization. At this revolutionary moment, called a ‘singular moment’ or ‘bifurcation point’, it is inherently impossible to determine in advance which direction change will take: whether the system will disintegrate into ‘chaos’ or leap to a new, more differentiated, higher level of ‘order’ or organization, called a ‘dissipative structure’.”

The essential phenomenon Prigogine seems to be attempting to capture in the use of the term "fluctuation", in all probability, is the instantaneous moment before a before a structural homogeneous fluid system (whale oil or silicon oil) spontaneously transforms into "Benard cell" structure when enough heat is added to the fluid.

More research, however, needs to be done on this term, to find its older usage in statistical mechanics.

1. Prigogine, Ilya. (1984). Order Out of Chaos – Man’s New Dialogue with Nature. New York: Bantam Books.

Further reading
● Glansdorff, P. and Prigogine, Ilya. (1971). Thermodynamic Theory of Structure, Stability and Fluctuations. John Wiley and Sons.
● Nicolis, G. and Prigogine, Ilya. (1977). Self-Organization in Non-Equilibrium Systems: From Dissipative Structures to Order Through Fluctuations. Wiley.
● Prigogine, Ilya. (1977). “Time, Structure and Fluctuations”, Nobel Lecture, Dec. 08.

External links
Fluctuation theorem – Wikipedia.

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