Related papers: CLT for Circular beta-Ensembles at High Temperatur…
The fluctuations in the ideal quantum gases are studied using the strongly intensive measures $\Delta[A,B]$ and $\Sigma[A,B]$ defined in terms of two extensive quantities $A$ and $B$. In the present paper, these extensive quantities are…
The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of…
The range of critical thermal fluctuations in classical bulk superconductors is extremely small and especially in low fields hardly experimentally inaccessible. With a new type of calorimeter we have been able to resolve a small lambda…
Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local…
Almost a century ago, Johnson and Nyquist presented evidence of fluctuating electrical current and the governing fluctuation dissipation theorem (FDT). Whether, likewise, temperature T can fluctuate is a controversial topic and has led to…
We give a simple proof of a central limit theorem for linear statistics of the Circular beta-ensembles which is valid at almost arbitrary mesoscopic scale and for functions of class C^3. As a consequence, using a coupling introduced by…
Recently many results namely the Fluctuation theorems (FT), have been discovered for systems arbitrarily away from equilibrium. Many of these relations have been experimentally tested. The system under consideration is usually driven out of…
In this article we investigate the behavior of multi-matrix unitary invariant models under a potential $V_\beta=\beta U+W$ when the inverse temperature $\beta$ becomes very large. We first prove, under mild hypothesis on the functionals…
In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…
We investigate the fluctuations of the free energy of the $2$-spin spherical Sherrington-Kirkpatrick model at critical temperature $\beta_c = 1$. When $\beta = 1$ we find asymptotic Gaussian fluctuations with variance $\frac{1}{6N^2}…
We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the…
Two-state models provide phenomenological descriptions of many different systems, ranging from physics to chemistry and biology. We investigate work fluctuations in an ensemble of two-state systems driven out of equilibrium under the action…
We study the extreme point process associated to the off-diagonal components in the matrix representation of the Gaussian $\beta$-Ensemble and prove its convergence to Poisson point process as $n\to +\infty$ when the inverse temperature…
Heat, work and entropy production: the statistical distribution of such quantities are constrained by the fluctuation theorems (FT), which reveal crucial properties about the nature of non-equilibrium dynamics. In this paper we report…
We carry out the asymptotic analysis of repulsive ensembles of N particles which are discrete analogues of continuous 1d log-gases or beta-ensembles of random matrix theory. The ensembles that we study have several groups of particles which…
The zero-temperature XX chain is studied with emphasis on the properties of a block of $L$ spins inside the chain. We investigate the quantum fluctuations resulting from the entanglement of the block with the rest of the chain using…
Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small' system exchanging energy with a bath is usually understood as a…
We address the question of transport of heat, in out-of-equilibrium systems. The experimental set-up consists in two coupled granular gas Non-Equilibrium Steady State (NESS) heat baths, in which Brownian-like rotors are imbedded. These…
In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation…
In this paper, we study fluctuations of conditionally centered statistics of the form $$N^{-1/2}\sum_{i=1}^N c_i(g(\sigma_i)-\mathbb{E}_N[g(\sigma_i)|\sigma_j,j\neq i])$$ where $(\sigma_1,\ldots ,\sigma_N)$ are sampled from a dependent…