Stability and Equilibrium States of Infinite Classical Systems
نویسندگان
چکیده
We prove that any stationary state describing an infinite classical system which is "stable" under local perturbations (and possesses some strong time clustering properties) must satisfy the "classical" KMS condition. (This in turn implies, quite generally, that it is a Gibbs state.) Similar results have been proven previously for quantum systems by Haag et al. and for finite classical systems by Lebowitz et al.
منابع مشابه
Extension of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Systems
The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...
متن کاملPower System Transient Stability Analysis Based on the Development and Evaluation Methods
A novel method to compute the stability region in power system transient stability analysis is presented. This method is based on the set analysis. The key to this method is to construct the Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) of a nonlinear system, using which we can compute the backward reachable set by applying the level set methods. The backward reachable set of...
متن کاملON THE STABILITY AND THRESHOLD ANALYSIS OF AN EPIDEMIC MODEL
We consider a mathematical model of epidemic spread in which the population is partitioned into five compartments of susceptible S(t), Infected I(t), Removed R(t), Prevented U(t) and the Controlled W(t). We assume each of the compartments comprises of cohorts of individuals which are identical with respect to the disease status. We derive five systems of equations to represent each of the ...
متن کاملStationary Non-Equilibrium States of Infinite Harmonic Systems
We investigate the existence, properties and approach to stationary non-equilibrium states of infinite harmonic crystals. For classical systems these stationary states are, like the Gibbs states, Gaussian measures on the phase space of the infinite system (analogues results are true for quantum systems). Their ergodic properties are the same as those of the equilibrium states: e.g. for ordered ...
متن کاملFuzzy Relational Matrix-Based Stability Analysis for First-Order Fuzzy Relational Dynamic Systems
In this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.In the first approach, the equilibrium point of the system is one of the centers of the related membership fu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004