Macroscopic control parameter for avalanche models of bursty transport

Similarity analysis is used to identify the control parameter RA for the subset of avalanching systems
that can exhibit self-organized criticality SOC. This parameter expresses the ratio of driving to
dissipation. The transition to SOC, when the number of excited degrees of freedom is maximal, is
found to occur when RA→0. This is in the opposite sense to Kolmogorov turbulence, thus
identifying a deep distinction between turbulence and SOC and suggesting an observable property
that could distinguish them. A corollary of this similarity analysis is that SOC phenomenology, that
is, power law scaling of avalanches, can persist for finite RA with the same RA→0 exponent if the
system supports a sufficiently large range of lengthscales, necessary for SOC to be a candidate for
physical RA finite systems.