Related papers: Effective statistical physics of Anosov systems
We present a new, elementary way to obtain axially symmetric Gaussian processes on the sphere, in order to accommodate for the directional anisotropy of global climate data in geostatistical analysis.
In this thesis we discuss some applications of the theory of Anosov systems to nonequilibrium statistical mechanics. In particular, we perform a perturbative check of the Gallavotti-Cohen fluctuation relation for a simple Anosov system; we…
We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as…
We develop a finite temperature field theory formalism in any dimension that has the filling fractions as the basic dynamical variables. The formalism efficiently decouples zero temperature dynamics from the quantum statistical sums. The…
Using the gauge-gravity duality, we argue that for a certain class of out-of-equilibrium steady-state systems in contact with a thermal background at a given temperature, the macroscopic physics can be captured by an effective thermodynamic…
Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a…
At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined…
Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Around a century ago it was realized that an extension to this type of dynamics can be obtained in…
The principle that heat spontaneously flows from higher temperature to lower temperature is a cornerstone of classical thermodynamics, often assumed to be independent of the sequence of interactions. While this holds true for macroscopic…
We study the existence of Anosov diffeomorphisms on complete open surfaces. We show that under the assumptions of density of periodic points and uniform geometry that such diffeomorphisms have a system of Margulis measures, which are a…
This paper investigates generalized thermodynamic relationships in physical systems where relevant macroscopic variables are determined by the exponential Kolmogorov-Nagumo average. We show that while the thermodynamic entropy of such…
In the process of analyzing the axiomatic principles underlying statistical physics, when modeling the most probable stationary macrostates of non-ergodic closed systems, a forecast was obtained about a possible limitation purview of the…
In this work we lead with expanding maps of the circle and Anosov diffeomorphisms on $\mathbb{T}^d, d \geq 2.$ We prove that, for these maps, \textit{constant periodic data} imply \textit{same periodic data of these maps and their…
The Fluctuation Relation for a stationary state, kept at constant energy by a deterministic thermostat - the Gallavotti-Cohen Theorem -- relies on the ergodic properties of the system considered. We show that when perturbed by an…
We classify quasiconformal Anosov flows whose strong stable and unstable distributions are at least two dimensional and the sum of these two distributions is smooth. We deduce from this classification result the complete classification of…
We consider perturbations of the Hamiltonian flow associated with the geodesic flow on a surface of constant negative curvature. We prove that, under a small perturbation, not necessarely of Hamiltonian character, the SRB measure associated…
We study functionals, such as heat and work, along trajectories of a class of multi-dimensional generalized Langevin systems in various limiting situations that correspond to different level of homogenization. These are the situations where…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
We introduce a generalization of the notion of Anosov representations by restricting to invariant closed geodesic subflows. Examples of such representations include many non-discrete representations with good geometric properties, such as…
We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by…