Related papers: An entropy for groups of intermediate growth
We consider a non-uniquely ergodic dynamical system given by a $\mathbb{Z}^{l}$-action (or $(\N\cup\{0\})^l$-action) $\tau$ on a non-empty compact metrisable space $\Omega$, for some $l\in\N$. Let (D) denote the following property: The…
Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…
We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…
Tsallis' non-extensive statistical mechanics is claimed to be the correct tool to describe the behaviour of low-dimensional dissipative maps at the edge of chaos. Indeed, many different approaches confirm that, for those systems, the…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
We analyze a contrasting dynamical behavior of Gibbs-Shannon and conditional Kullback-Leibler entropies, induced by time-evolution of continuous probability distributions. The question of predominantly purpose-dependent entropy definition…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power…
The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We…
Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. However, they are less…
In the pioneer work by Dimitrov-Haiden-Katzarkov-Kontsevich, they introduced various categorical analogies from classical theory of dynamical systems. In particular, they defined the entropy of an endofunctor on a triangulated category with…
Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…
Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…
Growth-fragmentation processes describe the evolution of systems of cells which grow continuously and fragment suddenly; they are used in models of cell division and protein polymerisation. Typically, we may expect that in the long run, the…
Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^{\alpha}$ potential. A mean field continuous integral equation is used to determine a saddle-point density…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
Boltzmannian statistical mechanics partitions the phase space of a system into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann's combinatorial…