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The goal of this paper is the identification of the physical processes at theorigin of the nonlinear behavior of a plasma conductor when an externalconstraint gradually departs the system from thermal equilibrium. This revealsthe presence of a self-organization scenario whose final product depends on themagnitude of the applied constraint. At first it appears a complexity whosestability is ensured by the presence of an electrical double layer. Byincreasing the external constraint the complexity transits into an autonomousstate whose existence is related to a rhythmic exchange of matter and energywith the surrounding environment, sustained and controlled by a proper dynamicsof the double layer. The results are potentially important for developing ageneral strategy of nonequilibrium physics, suggesting answers to challengingproblems concerning the mechanism that could explain the appearance ofself-organized complexities in laboratory and nature.

Plasma experiments with relevance for complexity science