Related papers: A topological classification of locally constant p…
We present a new general framework for metrization of Gromov-Hausdorff-type topologies on non-compact metric spaces. We also give easy-to-check conditions for separability and completeness and hence the measure theoretic requirements are…
Local temperature defined by a local canonical state of the respective subsystem, does not always exist in quantum many body systems. Here, we give some examples of how this breakdown of the temperature concept on small length scales might…
Temperature of a finite-sized system fluctuates due to the thermal fluctuations. However, a systematic mathematical framework for measuring or estimating the temperature is still underdeveloped. Here, we incorporate the estimation theory in…
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical…
This paper discusses the thermodynamic properties for certain time-dependent dynamical systems. In particular, we are interested in time-dependent dynamical systems with the specification property. We show that each time-dependent dynamical…
In this paper we propose a general functorial definition of the operation of \emph{local tropicalization} in commutative algebra. Let $R$ be a commutative ring, $\Gamma$ a finitely generated subsemigroup of a lattice, $\gamma : \Gamma…
We prove two relative local variational principles of topological pressure functions $P(T,\mathcal{F},\mathcal{U},y)$ and$P(T,\mathcal{F},\mathcal{U}|Y)$ for a given factor map $\pi$, an open cover $\mathcal{U} $ and a subadditive sequence…
We extend the circle theorem on the zeros of the partition function to a continuum system. We also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given…
The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on the category of sets. This enables the interpretation of a probabilistic programming language with primitives for sampling from discrete distributions.…
The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Several researchers have identified the thermodynamic…
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…
While temperature is well understood as an intensive quantity in standard thermodynamics, it is less clear whether the same holds in the presence of strong correlations, especially in the case of quantum systems, which may even display…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…
We derive thermodynamic functionals for spatially inhomogeneous magnetization on a torus in the context of an Ising spin lattice model. We calculate the corresponding free energy and pressure (by applying an appropriate external field using…
We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…
We prove a variational principle for the upper and lower metric mean dimension of level sets \[ \left\{x\in X: \lim_{n\to\infty}\frac{1}{n}\sum_{j=0}^{n-1}\varphi(f^{j}(x))=\alpha\right\} \] associated to continuous potentials $\varphi:X\to…
We consider the symmetry-resolved R\'{e}nyi and entanglement entropies for two-dimensional conformal field theories on a circle at nonzero temperature. We assume a unique ground state with a nonzero mass gap induced by the system's finite…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…
We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…