Related papers: Thermodynamic Formalism for Random Interval Maps w…

We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…

The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…

In this letter, we first redefine our formalism of the thermodynamic geometry introduced in [1,2] by changing coordinates of the thermodynamic space by means of Jacobian matrices. We then show that the geometrothermodynamics (GTD) is…

Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that "most" functions are optimized by measures supported on a periodic orbit, and it has…

We consider continuous maps $f:X\to X$ on compact metric spaces admitting inducing schemes of hyperbolic type introduced in [15] as well as the induced maps $\tilde{f}:\tilde{X}\to\tilde{X}$ and the associated tower maps $\hat{f}:\hat{X}…

We study ergodic-theoretic properties of coded shift spaces. A coded shift space is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of…

Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…

We study numerically the thermal conductivity coefficient $\kappa$ as a function of system length $L$ for several different quasi one dimensional models: classical gases of hard spheres with both longitudinal and transverse degrees of…

Transition Probability (fidelity) for pairs of density operators can be defined as "functor" in the hierarchy of "all" quantum systems and also within any quantum system. The introduction of "amplitudes" for density operators allows for a…

Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated.…

This paper has two themes that are intertwined: The first is the dynamics of certain piecewise affine maps on the Euclidean space that arise from a class of analog-to-digital conversion methods called Sigma-Delta quantization. The second is…

Dynamical Lie-algebraic method for the construction of local quantum invariants of motion in non-integrable many-body systems is proposed and applied to a simple but generic toy model, namely an infinite kicked $t-V$ chain of spinless…

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…

A new formulation of the thermodynamic field theory (TFT) is presented. In this new version, one of the basic restriction in the old theory, namely a closed-form solution for the thermodynamic field strength, has been removed. In addition,…

We study ergodic properties of certain piecewise smooth two-dimensional systems by constructing countable Markov partitions. Using thermodynamic formalism we prove exponential decay of correleations.

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…

We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…

We consider a stationary and ergodic random field $\{\omega(e) : e \in E_d\}$ that is parameterized by the edge set of the Euclidean lattice $\mathbb{Z}^d$, $d \geq 2$. The random variable $\omega(e)$, taking values in $[0, \infty)$ and…

We report a phase transition in the projected ensemble - the collection of post-measurement wavefunctions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a…

Non-Hermitian singularities are ubiquitous in non-conservative open systems. These singularities are often points of measure zero in the eigenspectrum of the system which make them difficult to access without careful engineering. Despite…