Related papers: The microscopic origin of abrupt transitions in in…

Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood.…

In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in a form of an abrupt first order transition. When the fraction of initial…

Recent advances have shown that introducing dependency interactions between two superconducting networks can trigger abrupt, hysteretic normal-superconductor phase transitions. In this study, we demonstrate that such behavior can also arise…

The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for increasing range of dependency couplings, different types of…

Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…

Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…

The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…

Integrated cyber-physical systems (CPSs), such as the smart grid, are increasingly becoming the underpinning technology for major industries. A major concern regarding such systems are the seemingly unexpected large-scale failures, which…

Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…

Compact stars above a critical stellar mass develop large scalar fields in some scalar-tensor theories. This scenario, called spontaneous scalarization, has been an intense topic of study since it passes weak-field gravity tests naturally…

The study of interdependent networks has recently experienced a boost with the development of experimentally testable materials that physically realize their critical behaviors, calling for systematic studies that go beyond the percolation…

A version of the second order phase transition theory, in which the Nernst theorem holds automatically, is proposed. The theory is constructed in terms of the order parameter and the (configurational) entropy. It faithfully reproduces the…

The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…

Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the…

Sudden and abrupt changes can occur in a nonlinear system within many fields of science when such a system crosses a tipping point and rapid changes of the system occur in response to slow changes in an external forcing. These can occur…

I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered…

Reliable functioning of infrastructure networks is essential for our modern society. Cascading failures are the cause of most large-scale network outages. Although cascading failures often exhibit dynamical transients, the modeling of…