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Hugo Touchette

Publications and source records attributed to Hugo Touchette.

64 records · Page 4Linked to original sources
arXiv2005

Asymptotics of superstatistics

Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special case. We develop here a technique that allows us to analyze the large energy asymptotics of the stationary distributions of general superstatistics. A saddle-point approximation is developed which relates this problem to a variational principle. Several examples are worked out in detail.

cond-mat.stat-mech↗
arXiv2005

Nonequivalent ensembles and metastability

This paper reviews a number of fundamental connections that exist between nonequivalent microcanonical and canonical ensembles, the appearance of first-order phase transitions in the canonical ensemble, and thermodynamic metastable behavior.

cond-mat.stat-mech↗
arXiv2004

Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model

Using the theory of large deviations, we analyze the phase transition structure of the Curie-Weiss-Potts spin model, which is a mean-field approximation to the Potts model. This analysis is carried out both for the canonical ensemble and the microcanonical ensemble. Besides giving explicit formulas for the microcanonical entropy and for the equilibrium macrostates with respect to the two ensembles, we analyze ensemble equivalence and nonequivalence at the level of equilibrium macrostates, relating these to concavity and support properties of the microcanonical entropy. The Curie-Weiss-Potts model is the first statistical mechanical model for which such a detailed and rigorous analysis has been carried out.

cond-mat.stat-mech↗
arXiv2004

Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model

We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel characterization takes effect at the level of the microcanonical and canonical equilibrium distributions of states. For this reason it may be viewed as a statistical characterization of nonequivalent ensembles which extends and complements the common thermodynamic characterization of nonequivalent ensembles based on nonconcave anomalies of the microcanonical entropy. By computing numerically both the microcanonical and canonical sets of equilibrium distributions of states of the BEG model, we show that for values of the mean energy where the microcanonical entropy is nonconcave, the microcanonical distributions of states are nowhere realized in the canonical ensemble. Moreover, we show that for values of the mean energy where the microcanonical entropy is strictly concave, the equilibrium microcanonical distributions of states can be put in one-to-one correspondence with equivalent canonical equilibrium distributions of states. Our numerical computations illustrate general results relating thermodynamic and statistical equivalence and nonequivalence of ensembles proved by Ellis, Haven, and Turkington [J. Stat. Phys. 101, 999 (2000)].

cond-mat.stat-mech↗
arXiv2003

Information-theoretic approach to the study of control systems

We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, takes the initial state of a system to be controlled and transforms it into a target state. In this sense, a controller can be thought of as an actuation channel that acts on inputs to produce desired outputs. In this transformation process, two different control strategies can be adopted: (i) the controller applies an actuation dynamics that is independent of the state of the system to be controlled (open-loop control); or (ii) the controller enacts an actuation dynamics that is based on some information about the state of the controlled system (closed-loop control). Using this communication channel model of control, we provide necessary and sufficient conditions for a system to be perfectly controllable and perfectly observable in terms of information and entropy. In addition, we derive a quantitative trade-off between the amount of information gathered by a closed-loop controller and its relative performance advantage over an open-loop controller in stabilizing a system. This work supplements earlier results [H. Touchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)] by providing new derivations of the advantage afforded by closed-loop control and by proposing an information-based optimality criterion for control systems. New applications of this approach pertaining to proportional controllers, and the control of chaotic maps are also presented.

physics.data-an↗
arXiv2002

Temperature fluctuations and mixtures of equilibrium states in the canonical ensemble

It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating inverse temperature. In this paper, we revisit this idea in connection with a detailed microscopic calculation of the energy and temperature fluctuations present in a finite vessel of perfect gas thermally coupled to a heat bath. We find that the probability density related to the inverse temperature of the gas has a form similar to a $χ^2$ density, and that the `mixed' Gibbs distribution inferred from this density is non-Gibbsian. These findings are compared with those obtained by a number of researchers who worked on mixtures of Gibbsian distributions in the context of velocity difference measurements in turbulent fluids as well as secondaries distributions in nuclear scattering experiments.

cond-mat.stat-mech↗
arXiv2002

When is a quantity additive, and when is it extensive?

The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are also defined.

cond-mat.stat-mech↗
arXiv2000

On a generalization of the logistic map

A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based on the construction of conjugacies. Moreover, it is shown that, despite the dissimilarity of their polynomial expressions, all the maps possess the same invariant density. Other algebraic properties of the family, which shows some relationship with the set of Tschebysheff polynomials, are also investigated.

nlin.CD↗
arXiv1999

Information-Theoretic Limits of Control

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of closed-loop control shows feedback control to be essentially a zero sum game: each bit of information gathered directly from a dynamical systems by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information (open-loop control). Consequences for the control of discrete binary systems and chaotic systems are discussed.

chao-dyn↗