Theory of phase-space density holes

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Abstract
A Bernstein–Green–Kruskal mode consisting of a depression or ’’hole’’ in the phase‐space density is shown to be a state of maximum entropy subject to constant mass, momentum, and energy. The parameter space of such holes is studied. The maximum entropy property is used to develop a simplified approximate analytic method as well as to infer the results of hole collisions including coalescing and decay. The maximum entropy property suggests that random, turbulent fluctuations tend to form into such self‐trapped structures and this nonperturbative concept is related to the physics of ’’clumps’’ which occur in a renormalized perturbative theory of turbulence.