Related papers: On the merit of a Central Limit Theorem-based appr…
We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short…
Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k going to 0 is discussed. It is shown that such tropical limit is well-adapted to analyse properties of systems with highly degenerated…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
We carefully examine the thermodynamic consequences of the repeated partial projection model for coupling a quantum system to an arbitrary series of environments under feedback control. This paper provides observational definitions of heat…
We investigate various possible definitions of an effective temperature for a particularly simple nonequilibrium stationary system, namely a heated Brownian particle suspended in a fluid. The effective temperature based on the fluctuation…
High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modelled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical…
The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…
For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-\kappa}$ for some constant $\kappa > 0$.…
A theoretical proposal that Coulomb-coupled quantum dots can be used as quantum probes to determine the temperature of a sample (i.e., an electronic reservoir) is proposed. Through the regulation of the positive or negative voltage bias in…
Temperature fluctuations of a finite system follows the Landau bound $\delta T^2 = T^2/C(T)$ where $C(T)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system…
The limiting temperature $T_{lim}$ of a series of nuclei is calculated employing a set of microscopic nuclear Equations of State (EoS). It is shown that the value of $T_{lim}$ is sensitive to the nuclear matter Equation of State used.…
This paper is concerned with normal approximation under relaxed moment conditions using Stein's method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of…
Conventional criticality-based quantum metrological schemes work only at zero or very low temperature because the quantum uncertainty around the quantum phase-transition point is generally erased by thermal fluctuations with the increase of…
Equilibrium probes have been widely used in various noisy quantum metrology schemes. However, such an equilibrium-probe-based metrology scenario severely suffers from the low-temperature-error divergence problem in the weak-coupling regime.…
We discuss the non-equilibrium critical phenomena in liquids, and the models for these phenomena based on local equilibrium and extended scaling assumptions. Special situations are proposed for experimental tests of the theory.…
Feedback cooling plays a critical role in stabilizing quantum systems and achieving low temperatures, where a key question is to determine the fundamental thermodynamic limits on cooling performance. We establish a fundamental bound on…
Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalisation in completely isolated quantum systems, such as cold-atom quantum simulators,…
The paper gives a bound on the generalization error of the Gibbs algorithm, which recovers known data-independent bounds for the high temperature range and extends to the low-temperature range, where generalization depends critically on the…
We briefly review the Thomas-Fermi statistical model of atoms in the classical non-relativistic formulation and in the generalised finite-nucleus relativistic formulation. We then discuss the classical generalisation of the model to finite…
In [Kozma-Toth, Ann. Probab. v 45, pp 4307-4347 (2017)] the weak CLT was established for random walks in doubly stochastic (or, divergence-free) random environments, under the following conditions: 1. Strict ellipticity assumed for the…