Santa Fe Institute

About: Santa Fe Institute is a nonprofit organization based out in Santa Fe, New Mexico, United States. It is known for research contribution in the topics: Population & Context (language use). The organization has 558 authors who have published 4558 publications receiving 396015 citations. The organization is also known as: SFI.

Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive

Abstract: Phase space can be constructed for N equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy S_(BG) ≡ -k Σ_i p_i ln p_i to be extensive, i.e., S_(BG)(N) ∝ N for N → ∞. In particular, if they are independent, S_(BG) is strictly additive, i.e., S_(BG)(N) = NS_(BG)(1), ∀N. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy S_q ≡ k[1 - Σi p^q_i]/(q - 1) (with S_1 = S_(BG)) for some special value of q ≠ 1 to be the one which is extensive [i.e., S_q(N) ∝ N for N → ∞]. Another concept which is relevant is strict or asymptotic scale-freedom (or scale-invariance), defined as the situation for which all marginal probabilities of the N-system coincide or asymptotically approach (for N → ∞) the joint probabilities of the (N - 1)-system. If each subsystem is a binary one, scale-freedom is guaranteed by what we hereafter refer to as the Leibnitz rule, i.e., the sum of two successive joint probabilities of the N-system coincides or asymptotically approaches the corresponding joint probability of the (N - 1)-system. The kinds of interplay of these various concepts are illustrated in several examples. One of them justifies the title of this paper. We conjecture that these mechanisms are deeply related to the very frequent emergence, in natural and artificial complex systems, of scale-free structures and to their connections with nonextensive statistical mechanics. Summarizing, we have shown that, for asymptotically scale-invariant systems, it is S_q with q ≠ 1, and not S_(BG), the entropy which matches standard, clausius-like, prescriptions of classical thermodynamics.

Quasi-resonant circulation regimes and hemispheric synchronization of extreme weather in boreal summer

Abstract: The recent decade has seen an exceptional number of high-impact summer extremes in the Northern Hemisphere midlatitudes. Many of these events were associated with anomalous jet stream circulation patterns characterized by persistent high-amplitude quasi-stationary Rossby waves. Two mechanisms have recently been proposed that could provoke such patterns: (i) a weakening of the zonal mean jets and (ii) an amplification of quasi-stationary waves by resonance between free and forced waves in midlatitude waveguides. Based upon spectral analysis of the midtroposphere wind field, we show that the persistent jet stream patterns were, in the first place, due to an amplification of quasi-stationary waves with zonal wave numbers 6–8. However, we also detect a weakening of the zonal mean jet during these events; thus both mechanisms appear to be important. Furthermore, we demonstrate that the anomalous circulation regimes lead to persistent surface weather conditions and therefore to midlatitude synchronization of extreme heat and rainfall events on monthly timescales. The recent cluster of resonance events has resulted in a statistically significant increase in the frequency of high-amplitude quasi-stationary waves of wave numbers 7 and 8 in July and August. We show that this is a robust finding that holds for different pressure levels and reanalysis products. We argue that recent rapid warming in the Arctic and associated changes in the zonal mean zonal wind have created favorable conditions for double jet formation in the extratropics, which promotes the development of resonant flow regimes.