相关论文: On the flexibility of complex systems

We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow…

The composite systems can be non-uniquely decomposed into parts (subsystems). Not all decompositions (structures) of a composite system are equally physically relevant. In this paper we answer on theoretical ground why it may be so. We…

We consider large-dimensional dynamical systems involving a linear force and a random force comprising both potential and non-conservative contributions. Such systems are known to exhibit a topological trivialization phase transition as the…

The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…

The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…

There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…

Out of thermal equilibrium, an environment imposes effective mechanical forces on microscopical nanofabricated devices, chemical or biological systems. Here we address the question of how to calculate these forces together with the response…

Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…

Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…

Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a…

Component systems - ensembles of realizations built from a shared repertoire of modular parts - are ubiquitous in biological, ecological, technological, and socio-cultural domains. From genomes to texts, cities, and software, these systems…

In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…

Dynamical phase transitions are defined through non-analyticities of the survival probability of an out-of-equilibrium time-evolving state at certain critical times. They ensue from zeros of the corresponding survival amplitude. By…

A simple weakly frequency dependent model for the dynamics of a population with a finite number of types is proposed, based upon an advantage of being rare. In the infinite population limit, this model gives rise to a non-smooth dynamical…

Mesoscopic systems in a slowly fluctuating environment are often well described by superstatistical models. We develop a generalized statistical mechanics formalism for superstatistical systems, by mapping the superstatistical complex…

LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…

Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…

Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…

(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…