Related papers: Is microcanonical ensemble stable?
We define restricted ensembles, called pico-canonical ensembles, for a statistical-mechanical description of the metastable and glassy phases. In this approach, time-evolution is Markovian, with temperature dependent rates. Below a…
Boltzmann introduced the microcanonical ensemble in 1868, \cite{Bo868-a}, and immediately attempted to give an example of a system whose stationary states would be described by the emsemble (as suggested also by his ergodic hypothesis). The…
The equivalence of thermodynamic results in the canonical and the microcanonical ensembles has been questioned in some calculations for spin models with long-range interactions. We show that these claims of inequivalence are related to an…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
The asymptotic equivalence of canonical and microcanonical ensembles is a central concept in statistical physics, with important consequences for both theoretical research and practical applications. However, this property breaks down under…
In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of…
Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy of the two ensembles. In [3]…
We show that the argument of Alexander and McTague, that the bcc crystalline structure is favored in those crystallization processes where the first order character is not too pronounced, is not correct. We find that any solution that…
We find sufficient conditions for commutative non-autonomous systems on certain metric spaces to be topologically stable. In particular, we prove that (i) Every mean equicontinuous, mean expansive system with strong average shadowing…
We generalize the de Almeida-Thouless line for the many-body Ising spin glass to the microcanonical ensemble and show that it coincides with the canonical one. This enables us to draw a complete microcanonical phase diagram of this model.
In this paper, we consider the volume enclosed by the microcanonical ensemble in phase space as a statistical ensemble. This can be interpreted as an intermediate image between the microcanonical and the canonical pictures. By maintaining…
We study fluctuations of the number of Bose condensed atoms in weakly interacting homogeneous and trapped gases. For a homogeneous system we apply the particle-number-conserving formulation of the Bogoliubov theory and calculate the…
We review here the microcanonical and canonical ensembles constructed on an underlying generalized quantum dynamics and the algebraic properties of the conserved quantities. We discuss the structure imposed on the microcanonical entropy by…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
The statistical properties of non-interacting bosons and fermions confined in trapping potentials are most easily obtained when the system may exchange energy and particles with a large reservoir (grand-canonical ensemble). There are…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…
We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient…
We construct stable configurations of n overlapping discs of radius r in a unit square, with r = O(1/n). By a result of Diaconis, Lebeau, and Michel, this result is best possible, up to a constant factor. A consequence is that the…
Recently, the full version of the Eigenstate Thermalization Hypothesis (ETH) has been systematized using Free Probability. In this paper, we present a detailed discussion of the Free Cumulants approach to many-body dynamics within the…
This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…