on brockett s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback the necessity of brockett s condition for stabilizability of nonlinear systems by smooth feedback is shown by an argument based on properties of a degree for set valued maps to persist when the class of controls is enlarged to include discontinuous feedback

existence of lipschitz and semiconcave control lyapunov functions given a locally lipschitz control system which is globally asymptotically controllable at the origin we construct a control lyapunov function for the system which is lipschitz on bounded sets and we deduce the existence of another one which is semiconcave and so locally lipschitz outside the origin the proof relies on value functions and nonsmooth calculus

statistical mechanics of classical systems with distinguishable particles the properties of classical models of distinguishable particles are shown to be identical to those of a corresponding system of indistinguishable particles without the need for ad hoc corrections an alternative to the usual definition of the entropy is proposed the new definition in terms of the logarithm of the probability distribution of the thermodynamic variables is shown to be consistent with all desired properties of the entropy and the physical properties of thermodynamic systems the factor of 1 n in the entropy connected with gibbs paradox is shown to arise naturally for both distinguishable and indistinguishable particles these results have direct application to computer simulations of classical systems which always use distinguishable particles such simulations should be compared directly to experiment in the classical regime without correcting them to account for indistinguishability

a general notion of global asymptotic controllability for time varying systems and its lyapunov characterization a general notion of global asymptotic controllability to a given equilibrium of a time varying system is introduced and is shown that this property is equivalent to the existence of a lower semicontinuous control lyapunov function the work constitutes an extension of albertini and sontag 1999 paper in same journal dealing with same subject under stricter hypotheses

construction of microcanonical entropy on thermodynamic pillars a question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume volume entropy also known as the gibbs entropy or as the logarithm of the density of states surface entropy also known as the boltzmann entropy rather than postulating them and investigating the consequence of each definition as is customary here we adopt a bottom up approach and construct the entropy expression within the microcanonical formalism upon two fundamental thermodynamic pillars i the second law of thermodynamics as formulated for quasistatic processes q t is an exact differential and ii the law of ideal gases pv k b nt the first pillar implies that entropy must be some function of the phase volume the second pillar singles out the logarithmic function among all possible functions hence the construction leads uniquely to the expression s k b ln that is the volume entropy as a consequence any entropy expression other than that of gibbs e g the boltzmann entropy can lead to inconsistencies with the two thermodynamic pillars we illustrate this with the prototypical example of a macroscopic collection of noninteracting spins in a magnetic field and show that the boltzmann entropy severely fails to predict the magnetization even in the thermodynamic limit the uniqueness of the gibbs entropy as well as the demonstrated potential harm of the boltzmann entropy provide compelling reasons for discarding the latter at once

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

feedback stabilization and lyapunov functions given a locally defined nondifferentiable but lipschitz lyapunov function we employ it in order to construct a discontinuous feedback law which stabilizes the underlying system to any given tolerance a converse result shows that suitable lyapunov functions of this type exist under mild assumptions we also establish that the feedback in question possesses a robustness property relative to measurement error despite the fact that it may not be continuous

links between asymptotic controllability and persistence of excitation for a class of time varying systems abstract for a class of nonlinear time varying parameterized systems we prove that persistence of excitation implies global asymptotic controllability to the equilibrium with respect to a set of parameters the result is used to derive sufficient conditions for global asymptotic controllability for composite systems

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

sampled data feedback practical semi global controllability and stabilization for time varying systems we deal with the problems of the closed loop controllability and stabilization for time varying systems whose dynamics are in general unbounded with respect to time it is shown that a general notion of global asymptotic controllability being in general non uniform with respect to initial values of time implies existence of a family of continuous control lyapunov functions and this enables the establishment of practical semi global closed loop controllability by means of a sampled data time varying feedback moreover the usual concept of global asymptotic controllability being uniform with respect to the initial values of time implies practical semi global stabilization by sampled data feedback the work is a continuation of a recent paper of the author in the same journal and extends krichman s 2000 result relying practical stabilization of time varying systems with bounded in time dynamics

planar nonlinear systems practical stabilization and hermes controllability condition abstract we analyze further some results from our recent work 1991 concerning the practical stabilizability problem by means of smooth feedback laws these results are used to establish that if a smooth planar nonlinear system satisfies the hermes controllability condition at its equilibrium then it can be practically stabilized

negative temperatures and the definition of entropy the concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics several researchers have identified the thermodynamic entropy exclusively with the volume entropy suggested by gibbs and have further concluded that by this definition negative temperatures violate the principles of thermodynamics we disagree with these conclusions we demonstrate that volume entropy is inconsistent with the postulates of thermodynamics for systems with non monotonic energy densities while a definition of entropy based on the probability distributions of macroscopic variables does satisfy the postulates of thermodynamics our results confirm that negative temperature is a valid extension of thermodynamics

dynamic uncertain causality graph for knowledge representation and probabilistic reasoning statistics base matrix and application graphical models for probabilistic reasoning are now in widespread use many approaches have been developed such as bayesian network a newly developed approach named as dynamic uncertain causality graph ducg is initially presented in a previous paper in which only the inference algorithm in terms of individual events and probabilities is addressed in this paper we first explain the statistic basis of ducg then we extend the algorithm to the form of matrices of events and probabilities it is revealed that the representation of ducg can be incomplete and the exact probabilistic inference may still be made a real application of ducg for fault diagnoses of a generator system of a nuclear power plant is demonstrated which involves variables most inferences take with a laptop computer the causal logic between inference result and observations is graphically displayed to users so that they know not only the result but also why the result obtained

comparison of canonical and microcanonical definitions of entropy abstract for more than 100 years one of the central concepts in statistical mechanics has been the microcanonical ensemble which provides a way of calculating the thermodynamic entropy for a specified energy a controversy has recently emerged between two distinct definitions of the entropy based on the microcanonical ensemble 1 the boltzmann entropy defined by the density of states at a specified energy and 2 the gibbs entropy defined by the sum or integral of the density of states below a specified energy a critical difference between the consequences of these definitions pertains to the concept of negative temperatures which by the gibbs definition cannot exist in this paper we call into question the fundamental assumption that the microcanonical ensemble should be used to define the entropy we base our analysis on a recently proposed canonical definition of the entropy as a function of energy we investigate the predictions of the boltzmann gibbs and canonical definitions for a variety of classical and quantum models our results support the validity of the concept of negative temperature but not for all models with a decreasing density of states we find that only the canonical entropy consistently predicts the correct thermodynamic properties while microcanonical definitions of entropy including those of boltzmann and gibbs are correct only for a limited set of models for models which exhibit a first order phase transition we show that the use of the thermodynamic limit as usually interpreted can conceal the essential physics

remarks on asymptotic controllability and sampled data feedback stabilization for autonomous systems a weak concept of sampled data feedback stabilization for the case of autonomous systems is presented and its lyapunov characterization is established sufficient conditions are derived for the existence of a time varying sampled data feedback exhibiting global stabilization for certain class of nonlinear systems

thermodynamic laws in isolated systems the recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying microcanonical thermostatistics here we provide a detailed comparison of the most commonly considered microcanonical entropy definitions focusing specifically on whether they satisfy or violate the zeroth first and second laws of thermodynamics our analysis shows that for a broad class of systems that includes all standard classical hamiltonian systems only the gibbs volume entropy fulfills all three laws simultaneously to avoid ambiguities the discussion is restricted to exact results and analytically tractable examples

an extension of artstein s theorem on stabilization by using ordinary feedback integrators abstract we prove that under suitable lyapunov like conditions a single input nonlinear system although it may not be stabilized by an ordinary state feedback law is dynamically stabilize by means of an ordinary feedback integrator

gibbs volume entropy is incorrect we show that the expression for the equilibrium thermodynamic entropy contains an integral over a surface in phase space and in so doing we confirm that negative temperature is a valid thermodynamic concept this demonstration disproves the claims of several recent papers that the gibbs entropy which contains an integral over a volume in phase space is the correct definition and that thermodynamics cannot be extended to include negative temperatures we further show that the gibbs entropy fails to satisfy the postulates of thermodynamics and that its predictions for systems with nonmonotonic energy densities of states are incorrect

asymptotic controllability and robust asymptotic stabilizability this paper deals with asymptotically controllable systems for which there exists no smooth stabilizing state feedback to investigate the robustness asymptotic stabilization property a new class of hybrid feedbacks with a continuous component and a discrete one is introduced the hybrid patchy feedbacks the notion of solutions is a generalization of pi solutions and euler solutions it is proved that the origin of all globally asymptotically controllable systems can be globally asymptotically stabilized via a hybrid feedback with robustness with respect to measurement noise actuator errors and external disturbances

in defense of negative temperature this pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature being derived from the usual often termed boltzmann definition of entropy first both the boltzmann and gibbs entropies must obey the same thermodynamic consistency relation second the boltzmann entropy does obey the second law of thermodynamics third there exists an integrating factor of the heat differential with both definitions of entropy