31 research outputs found
Thermodynamics of adiabatic feedback control
We study adaptive control of classical ergodic Hamiltonian systems, where the
controlling parameter varies slowly in time and is influenced by system's state
(feedback). An effective adiabatic description is obtained for slow variables
of the system. A general limit on the feedback induced negative entropy
production is uncovered. It relates the quickest negentropy production to
fluctuations of the control Hamiltonian. The method deals efficiently with the
entropy-information trade off.Comment: 6 pages, 1 figur
Exact scaling in the expansion-modification system
This work is devoted to the study of the scaling, and the consequent
power-law behavior, of the correlation function in a mutation-replication model
known as the expansion-modification system. The latter is a biology inspired
random substitution model for the genome evolution, which is defined on a
binary alphabet and depends on a parameter interpreted as a \emph{mutation
probability}. We prove that the time-evolution of this system is such that any
initial measure converges towards a unique stationary one exhibiting decay of
correlations not slower than a power-law. We then prove, for a significant
range of mutation probabilities, that the decay of correlations indeed follows
a power-law with scaling exponent smoothly depending on the mutation
probability. Finally we put forward an argument which allows us to give a
closed expression for the corresponding scaling exponent for all the values of
the mutation probability. Such a scaling exponent turns out to be a piecewise
smooth function of the parameter.Comment: 22 pages, 2 figure
Strengthened Lindblad inequality: applications in non equilibrium thermodynamics and quantum information theory
A strengthened Lindblad inequality has been proved. We have applied this
result for proving a generalized -theorem in non equilibrium thermodynamics.
Information processing also can be considered as some thermodynamic process.
From this point of view we have proved a strengthened data processing
inequality in quantum information theory.Comment: 7 pages, revte
Spin-glass model with partially annealed asymmetric bonds
We have considered the two-spin interaction spherical spin-glass model with
asymmetric bonds (coupling constants). Besides the usual interactions between
spins and bonds and between the spins and a thermostat with temperature
there is also an additional factor: the bonds are not assumed
random {\it a priori} but interact with some other thermostat at the
temperature . We show that when the bonds are frozen with respect to the
spins a first order phase transition to a spin-glass phase occurs, and the
temperature of this transition tends to zero if is large. Our analytical
results show that a spin-glass phase can exist in mean-field models with
nonrelaxational dynamics.Comment: 10 pages, late
Nonlinear deterministic equations in biological evolution
We review models of biological evolution in which the population frequency
changes deterministically with time. If the population is self-replicating,
although the equations for simple prototypes can be linearised, nonlinear
equations arise in many complex situations. For sexual populations, even in the
simplest setting, the equations are necessarily nonlinear due to the mixing of
the parental genetic material. The solutions of such nonlinear equations
display interesting features such as multiple equilibria and phase transitions.
We mainly discuss those models for which an analytical understanding of such
nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy
Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal noise
To understand the sample-to-sample fluctuations in disorder-generated
multifractal patterns we investigate analytically as well as numerically the
statistics of high values of the simplest model - the ideal periodic
Gaussian noise. By employing the thermodynamic formalism we predict the
characteristic scale and the precise scaling form of the distribution of number
of points above a given level. We demonstrate that the powerlaw forward tail of
the probability density, with exponent controlled by the level, results in an
important difference between the mean and the typical values of the counting
function. This can be further used to determine the typical threshold of
extreme values in the pattern which turns out to be given by
with . Such observation provides a
rather compelling explanation of the mechanism behind universality of .
Revealed mechanisms are conjectured to retain their qualitative validity for a
broad class of disorder-generated multifractal fields. In particular, we
predict that the typical value of the maximum of intensity is to be
given by , where is the
corresponding singularity spectrum vanishing at . For the
noise we also derive exact as well as well-controlled approximate
formulas for the mean and the variance of the counting function without
recourse to the thermodynamic formalism.Comment: 28 pages; 7 figures, published version with a few misprints
corrected, editing done and references adde
Finite size corrections in the random energy model and the replica approach
We present a systematic and exact way of computing finite size corrections
for the random energy model, in its low temperature phase. We obtain explicit
(though complicated) expressions for the finite size corrections of the overlap
functions. In its low temperature phase, the random energy model is known to
exhibit Parisi's broken symmetry of replicas. The finite size corrections given
by our exact calculation can be reproduced using replicas if we make specific
assumptions about the fluctuations (with negative variances!) of the number and
sizes of the blocks when replica symmetry is broken. As an alternative we show
that the exact expression for the non-integer moments of the partition function
can be written in terms of coupled contour integrals over what can be thought
of as "complex replica numbers". Parisi's one step replica symmetry breaking
arises naturally from the saddle point of these integrals without making any
ansatz or using the replica method. The fluctuations of the "complex replica
numbers" near the saddle point in the imaginary direction correspond to the
negative variances we observed in the replica calculation. Finally, our
approach allows one to see why some apparently diverging series or integrals
are harmless.Comment: 23 pages, 1 figure, revised version 11 December 201
Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets
A theory of exceptional extreme events, characterized by their abnormal sizes
compared with the rest of the distribution, is presented. Such outliers, called
"dragon-kings", have been reported in the distribution of financial drawdowns,
city-size distributions (e.g., Paris in France and London in the UK), in
material failure, epileptic seizure intensities, and other systems. Within our
theory, the large outliers are interpreted as droplets of Bose-Einstein
condensate: the appearance of outliers is a natural consequence of the
occurrence of Bose-Einstein condensation controlled by the relative degree of
attraction, or utility, of the largest entities. For large populations, Zipf's
law is recovered (except for the dragon-king outliers). The theory thus
provides a parsimonious description of the possible coexistence of a power law
distribution of event sizes (Zipf's law) and dragon-king outliers.Comment: Latex file, 16 pages, 1 figur