Similarity of fluctuations in systems exhibiting Self-Organized Criticality

Solid State Section and Solid Earth Physics Institute, Physics Department, University of Athens Panepistimiopolis, Zografos 157 84, Athens, Greece, EU

^a pvaro@otenet.gr

Received: 28 June 2011
Accepted: 1 September 2011

Abstract

The time-series of avalanches in three systems exhibiting SOC are analyzed in natural time χ. In two of them, i.e., ricepiles and magnetic flux penetration in thin films of YBa₂Cu₃O_7−x, the data come from laboratory measurements, while the third one is a deterministic model mimicking stick-slip phenomena. We show that their scaled distributions for the variance κ₁ of natural time exhibit an exponential tail as previously found for the order parameter in seismicity and in other non-equilibrium or equilibrium critical systems. Upon considering the entropy S₋ in natural time under time reversal, the following important difference is found: In ricepiles evolving to the critical state, S₋ is systematically larger than the entropy S in natural time, while in YBa₂Cu₃O_7−x no systematic difference between S₋ and S is found.