Entropy production and self-organized criticality in earthquake dynamics

General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Three-line summary. We test the hypothesis that maximum entropy production is a potential thermodynamic driver for self-organised criticality in earthquake dynamics. The result is positive, with the caveat that the MEP state is near but just below the strict critical point, where system memory in the form of fractal patterns in the strain field emerge as a consequence of a finite order parameter. Media Abstract. Reliable earthquake prediction remains the 'holy grail' of seismology. For now the research frontier remains probabilistic: can we forecast the population dynamics better than a series of random events with aftershocks? We apply methods developed in thermodynamics to the problem of earthquake population dynamics, using a simple computer model that reproduces many of the characteristics Made available online through Edinburgh Research Explorer 2 of real earthquake populations. The system, in the absent of other constraints, tunes itself spontaneously to a near-critical state where individual events are inherently difficult, if not impossible, to predict reliably, but there may be some forecasting power at a lower level of probability. Summary. We derive an analytical expression for entropy production in earthquake populations based on Dewar's formulation, including gradient (tectonic forcing) and fluctuation (earthquake population) terms, and apply it to the Olami-Feder-Christensen (OFC) numerical model for earthquake dynamics. Assuming the commonly-observed power-law rheology between driving stress and remote strain rate, we test the hypothesis that maximum entropy production is a thermodynamic driver for self-organized 'criticality' (SOC) in the model. Maximum entropy production occurs when the global elastic strain is near-critical, with small relative fluctuations in macroscopic strain energy expressed by a low seismic efficiency, and broad-bandwidth power-law scaling of frequency and rupture area. These phenomena, all as observed in natural earthquake populations, are hallmarks of the broad conceptual definition of SOC, (which includes self-organizing systems in a near but strictly …