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M Courbage

Publications and source records attributed to M Courbage.

5 recordsLinked to original sources
PubMed2004

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons.

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.

Action Potentials↗
PubMed1983

Intrinsic randomness and intrinsic irreversibility in classical dynamical systems.

We continue our previous work on dynamic "intrinsically random" systems for which we can derive dissipative Markov processes through a one-to-one change of representation. For these systems, the unitary group of evolution can be transformed in this way into two distinct Markov processes leading to equilibrium for either t--> + infinity or t--> - infinity. To lift the degeneracy, we first formulate the second principle as a selection rule that is meaningful in intrinsically random systems. For these systems, this excludes a set of unrealizable states. As a result of this exclusion, permitted initial conditions correspond to a set of states that is not invariant through velocity inversion. In this way, the time-reversal symmetry of dynamics is broken and these systems acquire a new feature we may call "intrinsic irreversibility." The set of admitted initial conditions can be characterized by an entropy displaying the amount of information necessary for their preparation. The initial conditions selected by the second law correspond to a finite amount of information, while the initial conditions that are rejected correspond to an infinite amount of information and are therefore "impossible." We believe that our formulation permits a microscopic formulation of the second law of thermodynamics for well-defined classes of dynamical systems.

Journal Article↗
PubMed1979

Lyapounov variable: Entropy and measurement in quantum mechanics.

We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables-i.e., dynamical variables varying monotonically in time without becoming contradictory. It has been found that such variables can exist in an extended framework of classical dynamics, provided that the dynamical motion is suitably unstable. In this paper we begin to extend these results to quantum mechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantum mechanics. However, if the Hamiltonian has certain well-defined spectral properties, such variables can be defined but only as a nonfactorizable superoperator. Necessary nonfactorizability of such entropy operators M has the consequence that they cannot preserve the class of pure states. Physically, this means that the distinguishability between pure states and corresponding mixtures must be lost in the case of a quantal system for which the algebra of observables can be extended to include a new dynamical variable representing nonequilibrium entropy. We discuss how this result leads to a solution of the quantum measurement problem. It is also found that the question of existence of entropy of superoperators M is closely linked to the problem of defining an operator of time in quantum mechanics.

Journal Article↗
PubMed1979

From deterministic dynamics to probabilistic descriptions.

THE PRESENT WORK IS DEVOTED TO THE FOLLOWING QUESTION: What is the relationship between the deterministic laws of dynamics and probabilistic description of physical processes? It is generally accepted that probabilistic processes can arise from deterministic dynamics only through a process of "coarse graining" or "contraction of description" that inevitably involves a loss of information. In this work we present an alternative point of view toward the relationship between deterministic dynamics and probabilistic descriptions. Speaking in general terms, we demonstrate the possibility of obtaining (stochastic) Markov processes from deterministic dynamics simply through a "change of representation" that involves no loss of information provided the dynamical system under consideration has a suitably high degree of instability of motion. The fundamental implications of this finding for statistical mechanics and other areas of physics are discussed. From a mathematical point of view, the theory we present is a theory of invertible, positivity-preserving, and necessarily nonunitary similarity transformations that convert the unitary groups associated with deterministic dynamics to contraction semigroups associated with stochastic Markov processes. We explicitly construct such similarity transformations for the so-called Bernoulli systems. This construction illustrates also the construction of the so-called Lyapounov variables and the operator of "internal time," which play an important role in our approach to the problem of irreversibility. The theory we present can also be viewed as a theory of entropy-increasing evolutions and their relationship to deterministic dynamics.

Journal Article↗