Related papers: Inner Functions, Composition Operators, Symbolic D…
The study of escape rates for a ball in a dynamical systems has been much studied. Understanding the asymptotic behavior of the escape rate as the radius of the ball tends to zero is an especially subtle problem. In the case of hyperbolic…
We study the thermodynamic formalism of systems where the potential depends randomly on an exterior system. We define the {\em pressure out of equilibrium} for such a family of potentials, and prove a corresponding variational principle. We…
Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more…
I apply the thermodynamics of radiation to Dyson spheres as machines that do work or computation, and examine their observational consequences. I identify four properties of Dyson spheres that complicate typical analyses: globally, they may…
In this paper, we study the thermodynamics of short-range central potentials, namely, the Lee-Wick potential, and the Plasma potential. In the first part of the paper we obtain the numerical solution for the orbits equation for these…
Let $X = G/\Gamma$ be a quotient of a real Lie group by a non-uniform lattice. Consider a one-parameter subgroup $F$ of $G$ that is $\operatorname{Ad}$-diagonalizable over $\mathbb{C}$ and whose action on $(X,m_X)$ is mixing. In this…
We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density,…
Thermal behavior in subsystems of closed quantum systems is commonly attributed to dynamical chaos, quantum ergodicity, canonical typicality, or the eigenstate thermalization hypothesis, suggesting a fundamentally statistical origin of…
Spintronics on flat surfaces has been studied over the years, and the scenario is relatively well-known; however, there is a lack of information when we consider non-flat surfaces. In this paper, we are concerned about the spin dynamics of…
Given a finite-to-one map acting on a compact metric space, one classically constructs for each potential in an appropriate Banach space of functionsa transfer operator acting on functions. Under suitable condition, the…
We investigate the basic thermal, mechanical and structural properties of body centred cubic iron ($\alpha$-Fe) at several temperatures and positive loading by means of Molecular Dynamics simulations in conjunction with the embedded-atom…
Periodically driven Floquet quantum many-body systems have revealed new insights into the rich interplay of thermalization, and growth of entanglement. The phenomenology of dynamical freezing, whereby a translationally invariant many-body…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
We study the linear dynamics of composition operators induced by measurable transformations on finite measure spaces, with particular emphasis on operators induced by odometers. Our first main result shows that, on a finite measure space,…
Using Hecke triangle surfaces of finite and infinite area as examples, we present techniques for thermodynamic formalism approaches to Selberg zeta functions with unitary finite-dimensional representations $(V,\chi)$ for hyperbolic surfaces…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the…
This paper reports on constructive approximation methods for three classes of holomorphic functions on the unit disk which are closely connected each other: the class of starlike and spirallike functions, the class of semigroup generators,…
In this article, we continue the structural study of factor maps betweeen symbolic dynamical systems and the relative thermodynamic formalism. Here, one is studying a factor map from a shift of finite type $X$ (equipped with a potential…
We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wavefunction renormalization and…