Related papers: Generalized R\'enyi Entropy and Structure Detectio…
We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
One of the outstanding problems in non-equilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that…
In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of…
We consider general Exponential Random Graph Models (ERGMs) where the sufficient statistics are functions of homomorphism counts for a fixed collection of simple graphs $F_k$. Whereas previous work has shown a degeneracy phenomenon in dense…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
A generalization of the entropy production rate is proposed $\Pi_q$ in non-equilibrium systems by extending the formalism of classical stochastic thermodynamics to regimes with non-Gaussian fluctuations. Through the R\'enyi entropy $S_q$ ,…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
We derive several new results for Renyi entropy, $S_n$, across generic entangling surfaces. We establish a perturbative expansion of the Renyi entropy, valid in generic quantum field theories, in deformations of a given density matrix. When…
We calculate analytically the Renyi entropy for the zeta-urn model with a Gibbs measure definition of the micro-state probabilities. This allows us to obtain the singularities in the R\'enyi entropy from those of the thermodynamic…
Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug-design. Current techniques suffer from being model specific,…