Related papers: Effective Gibbs state for averaged observables
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
Given a mixed quantum state $\rho$ of a qudit, we consider any observable $M$ as a kind of `thermometer' in the following sense. Given a source which emits pure states with these or those distributions, we select such distributions that the…
A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous…
The R\'enyi entanglement entropy is calculated exactly for mode-partitioned isolated systems such as the two-mode squeezed state and the multi-mode Silbey-Harris polaron ansatz state. Effective thermodynamic descriptions of the correlated…
In this paper we compute the effective Lagrangian of static gravitational fields interacting with thermal fields of generalized electrodynamics at high temperature. We employ the usual Matsubara imaginary-time formalism to obtain a closed…
The paper proposes some robust estimators of the finite population mean. Such estimators are particularly suitable in the presence of some outlying observations. Included as special cases of our general result are robust versions of the…
Many Gibbs measures with mean field interactions are known to be chaotic, in the sense that any collection of $k$ particles in the $n$-particle system are asymptotically independent, as $n\to\infty$ with $k$ fixed or perhaps $k=o(n)$. This…
We propose to interpret machine learning functions as physical observables, opening up the possibility to apply "standard" statistical-mechanical methods to outputs from neural networks. This includes histogram reweighting and finite-size…
The amount of extractable work from a physical system is fundamentally connected to the information available about its state, as illustrated by Maxwell's demon and the Gibbs paradox. In standard thermodynamic protocols involving…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…
We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Hal\'asz. Several…
Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…
The problem of gauge independent definition of effective gravitational field is considered from the point of view of the process of measurement. Under assumption that dynamics of the measuring apparatus can be described by the ordinary…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…
The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system (HIPS). It is shown that the McKean-Vlasov…
A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects.…
In principle, observables as for example the sphaleron rate or the tunneling rate in a first-order phase transition are gauge-independent. However, in practice a gauge dependence is introduced in explicit perturbative calculations due to…
We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations…
In the present paper we study the entanglement properties of thermal (a.k.a. Gibbs) states of quantum harmonic oscillator systems as functions of the Hamiltonian and the temperature. We prove the physical intuition that at sufficiently high…