Related papers: Transience and thermodynamic formalism for infinit…

In this paper, we study the driven-dissipative p-spin models for $p\geq 2$. In thermodynamics limit, the equation of motion is derived by using a semiclassical approach. The long-time asymptotic states are obtained analytically, which…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…

We consider a class of simple one parameter families of interval maps, and we study how metric (resp. topological) entropy changes as the parameter varies. We show that in many cases the entropy displays a semi-regular behaviour, i.e. it is…

We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the…

Interpreting partial information collected from systems subject to noise is a key problem across scientific disciplines. Theoretical frameworks often focus on the dynamics of variables that result from coarse-graining the internal states of…

I discuss the analytic structure of thermodynamic quantities for complex values of thermodynamic variables within Landau theory. In particular, the singularities connected with phase transitions of second order, first order and cross over…

Skew product systems with monotone one-dimensional fibre maps driven by piecewise expanding Markov interval maps may show the phenomenon of intermingled basins. To quantify the degree of intermingledness the uncertainty exponent and the…

First-order phase transitions are commonly associated with a discontinuous behavior of some of the thermodynamic variables and the presence of a latent heat. In the present study it is shown that this is not necessarily the case. Using…

Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…

A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite sub-matrices of an infinite nonnegative…

We study weighted transfer operators associated to a piecewise expanding map on a compact manifold, and a piecewise Holder weight, acting on Sobolev spaces. We bound the essential spectral radius in terms of a topological pressure for a…

Large-scale atomistic simulations can produce extreme volumes of information in the form of long trajectories. Reliably and automatically extracting key information from such datasets remains a formidable challenge, especially as it…

Let $I\subset\mathbb{R}$ be an interval and $T_a:[0,1]\to[0,1]$, $a\in I$, a one-parameter family of piecewise expanding maps such that for each $a\in I$ the map $T_a$ admits a unique absolutely continuous invariant probability measure…

A common approach to quantify excess dissipation in slowly driven thermodynamic processes is through the use of a Riemannian metric on the space of control parameters, where optimal driving protocols follow geodesics. Near phase…

In this paper, we study the thermodynamic formalism of interval maps $f$ with sufficient regularity, for a sub class $\mathcal{U}$ composed of upper semi-continuous potentials which includes both H\"{o}lder and geometric potentials. We show…

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged…

Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation…

We consider the multifractal analysis of the pointwise dimension for Gibbs measures on countable Markov shifts. Our paper analyses the set of non-analytic points or phase transitions of the multifractal spectrum. By Sarig's thermodynamic…

We present a theory of second phase conductive filaments in phase transformable systems; applications include threshold switches, phase change memory, and shunting in thin film structures. We show that the average filament parameters can be…

We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of…