Related papers: Effective Gibbs state for averaged observables
We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et…
For thermal systems, standard perturbation theory breaks down because of the absence of stable, observable asymptotic states. We show, how the introduction of {\it statistical} quasi-particles (stable, but not observable) gives rise to a…
We present two independent approaches for computing the thermodynamics for classical particles interacting via the Moser--Calogero potential. Combining the results we propose the form of equation of state or, what is equivalent, the…
The effective approach is applied to the analysis of inflationary magnetogenesis. Rather than assuming a particular underlying description, all the generally covariant terms potentially appearing with four space-time derivatives in the…
We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for…
As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium…
In the present paper which follows our previous paper ``Mathematical models for passive imaging I: general background'', we discuss the case of surface waves in a medium which is stratified near its boundary at some scale comparable to the…
An open quantum system interacting with a heat bath at given temperature is expected to reach the mean force Gibbs (MFG) state as a steady state. The MFG state is given by tracing out the bath degrees of freedom from the equilibrium Gibbs…
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin…
For quadratic-like maps, we show a phenomenon of sensitive dependence of geometric Gibbs states: There are analytic families of quadratic-like maps for which an arbitrarily small perturbation of the parameter can have a definite effect on…
Recent progress has shown that the generalization error of the Gibbs algorithm can be exactly characterized using the symmetrized KL information between the learned hypothesis and the entire training dataset. However, evaluating such a…
In this paper, we developed a thermodynamically consistent approach to account for the Gibbs energy of pure metallic element with thermal vacancy over wide temperature range. Taking body centered cubic (bcc) W for a demonstration, the…
We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and…
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…
Thermal energy agitates all matter and its competition with ordering tendencies is one of the most fundamental organizing principles in the physical world. Thus, it is natural to enquire if an effective temperature could result when…
We derive a general information-theoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement…
We combine traditional pointer-based simultaneous measurements of conjugate observables with the concept of quantum Brownian motion of multipartite systems to phenomenologically model simultaneous measurements of conjugate observables in a…
Simple classical thermodynamic approach to the general description of metastable states is presented. It makes possible to calculate the explicit dependence of the Gibbs free energy on temperature, to calculate the heat capacity, the…