Related papers: Is microcanonical ensemble stable?
Stationary states of quantum many-body Hamiltonians are invariant under the Hamiltonian evolution. Besides ground and thermal states, this class includes microcanonical ensembles that are of fundamental importance in statistical physics. We…
We show insurmountable contradictions which arise if statistical ensembles are considered a consequence of the influence of the environment of the physical systems. We regard the multiplicity of states with a definite energy value as a…
We consider a small Hamiltonian system strongly interacting with a much larger Hamiltonian system (the bath), while being driven by both a time-dependent control parameter and non-conservative forces. The joint system is assumed to be…
We derive the microcanonical ensemble from the Maximum Entropy Principle (MEP) using the phase space volume entropy of P. Hertz. Maximizing this entropy with respect to the probability distribution with the constraints of normalization and…
We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)] in the microcanonical…
This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end…
Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including…
The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, traditionally only the canonical and grand canonical ensembles have been used. In this…
It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e.,…
Microcanonical description is characterized by the presence of an internal symmetry closely related with the dynamical origin of this ensemble: the reparametrization invariance. Such symmetry possibilities the development of a non…
A generalization of the microcanonical ensemble suggests a simple strategy for the simulation of first order phase transitions. At variance with flat-histogram methods, there is no iterative parameters optimization, nor long waits for…
We study the stability of ultracompact boson stars admitting light rings combining a perturbative analysis with 3+1 numerical-relativity simulations with and without symmetry assumptions. We observe excellent agreement between all…
For classical Hamiltonian N-body systems with mildly regular pair interaction potential it is shown that when N tends to infinity in a fixed bounded domain, with energy E scaling quadratically in N proportional to e, then Boltzmann's…
A simple, exactly solvable statistical model is presented for the description of baryonic matter in the thermodynamic conditions associated to the evolution of core-collapsing supernova. It is shown that the model presents a first order…
Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions.…
Near-extremal black membranes with topological (baryonic) $U(1)_B$ charge of M-theory compactified on the coset space $M^{1,1,0}$ are stable. $M^{1,1,0}$ coset is a ${\mathbb Z}_2$-invariant truncation of a larger $Q^{1,1,1}$ coset, with…
We prove that, if $C$ is a smooth projective curve over the complex numbers, and $E$ is a stable vector bundle on $C$ whose slope does not lie in the interval $[-1,n-1]$, then the associated tautological bundle $E^{[n]}$ on the symmetric…
In this paper, we use a variety of mathematical techniques to explore existence, local stability, and global stability of equilibria in abstract models of mitochondrial metabolism. The class of models constructed is defined by the…
The Ensemble of trajectories $x(0 \leq t \leq T)$ produced by the Markov generator $M$ can be considered as 'Canonical' for the following reasons : (C1) the probability of the trajectory $x(0 \leq t \leq T)$ can be rewritten as the…
We consider a system of globally coupled rotors, described by a set of Langevin equations, and examine stability of the incoherent phase. The corresponding Fokker-Planck equation, providing a unified description of microcanonical and…