Estimation of local microcanonical averages in two lattice mean-field models using coupling techniques

Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals

We consider a generic classical many particle system described by an autonomous Hamiltonian $H(x^{_1},...,x^{_{N+2}})$ which, in addition, has a conserved quantity $V(x^{_1},...,x^{_{N+2}})=v$, so that the Poisson bracket $\{H,V \}$ vanishes. We derive in detail the microcanonical expressions for entropy and temperature. We show that both of these quantities depend on multidimensional integrals over submanifolds given by the intersection of the constant energy hypersurfaces with those defined by $V(x^{_1},...,x^{_{N+2}})=v$. We show that temperature and higher order derivatives of entropy are …

Geometric microcanonical theory of two-dimensional Truncated Euler flows

This paper presents a geometric microcanonical ensemble perspective on two-dimensional Truncated Euler flows, which contain a finite number of (Fourier) modes and conserve energy and enstrophy. We explicitly perform phase space volume integrals over shells of constant energy and enstrophy. Two applications are considered. In a first part, we determine the average energy spectrum for highly condensed flow configurations and show that the result is consistent with Kraichnan's canonical ensemble description, despite the fact that no thermodynamic limit is invoked. In a second part, we compute the…

Higher time derivatives in the microcanonical ensemble describe dynamics of flux-coupled classical and quantum oscillators

We show that it is possible to consistently describe dynamical systems, whose equations of motion are of degree higher than two, in the microcanonical ensemble, even if the higher derivatives aren't coordinate artifacts. Higher time derivatives imply that there are more than one Hamiltonians, conserved quantities due to time translation invariance, and, if the volume in phase space, defined by their intersection, is compact, microcanonical averages can be defined and there isn't any instability, in the sense of Ostrogradsky, even though each Hamiltonian, individually, may define a non-compact …

无标记网络中的系综不等价性与相变

Ensemble inequivalence and phase transitions in unlabeled networks

该研究发现无标记网络正则系综中存在由微正则熵非凹性导致的一级相变，揭示了临界点上下系综等价性的差异及无标记网络无渗流相变，指出系综选择作为真实网络零模型的问题值得关注。