Nonequilibrium statistical mechanics of the turbulent energy cascade: Irreversibility and response functions.

The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a scenario dubbed "direct energy cascade." From a statistical mechanics point of view, the cascade picture prevents the existence of detailed balance, which holds at equilibrium, e.g.

Revealing the Nonequilibrium Nature of a Granular Intruder: The Crucial Role of Non-Gaussian Behavior.

The characterization of the distance from equilibrium is a debated problem in particular in the treatment of experimental signals. If the signal is a one-dimensional time series, such a goal becomes challenging. A paradigmatic example is the angular diffusion of a rotator immersed in a vibro-fluidized granular gas.

Correlation, response and entropy approaches to allosteric behaviors: a critical comparison on the ubiquitin case.

Correlation analysis and its close variant principal component analysis are tools widely applied to predict the biological functions of macromolecules in terms of the relationship between fluctuation dynamics and structural properties. However, since this kind of analysis does not necessarily imply causation links among the elements of the system, its results run the risk of being biologically misinterpreted. By using as a benchmark the structure of ubiquitin, we report a critical comparison of correlation-based analysis with the analysis performed using two other indicators, response function and transfer entropy, that quantify the causal dependence.

Extracting causation from millennial-scale climate fluctuations in the last 800 kyr.

The detection of cause-effect relationships from the analysis of paleoclimatic records is a crucial step to disentangle the main mechanisms at work in the climate system. Here, we show that the approach based on the generalized Fluctuation-Dissipation Relation, complemented by the analysis of the Transfer Entropy, allows the causal links to be identified between temperature, CO[Formula: see text] concentration and astronomical forcing during the glacial cycles of the last 800 kyr based on Antarctic ice core records. When considering the whole spectrum of time scales, the results of the analysis suggest that temperature drives CO[Formula: see text] concentration, or that are both driven by the common astronomical forcing.