48,775 research outputs found
Entropy increase in switching systems
The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipative affine maps has a pullback attractor consisting of singleton component sets. This entails that the complexity of the control sequence and switched dynamics, as quantified by the topological entropy, coincide. In this paper we extend the previous framework to pullback attractors with nontrivial components sets in order to gain further insights in that relation. This calls, in particular, for distinguishing two distinct contributions to the complexity of the switched dynamics. One proceeds from trajectory segments connecting different component sets of the attractor; the other contribution proceeds from trajectory segments within the component sets. We call them âmacroscopicâ and âmicroscopicâ complexity, respectively, because only the first one can be measured by our analytical tools. As a result of this picture, we obtain sufficient conditions for a switching system to be more complex than its unswitched subsystems, i.e., a complexity analogue of Parrondoâs paradox
Quantifying sudden changes in dynamical systems using symbolic networks
We characterise the evolution of a dynamical system by combining two
well-known complex systems' tools, namely, symbolic ordinal analysis and
networks. From the ordinal representation of a time-series we construct a
network in which every node weights represents the probability of an ordinal
patterns (OPs) to appear in the symbolic sequence and each edges weight
represents the probability of transitions between two consecutive OPs. Several
network-based diagnostics are then proposed to characterize the dynamics of
different systems: logistic, tent and circle maps. We show that these
diagnostics are able to capture changes produced in the dynamics as a control
parameter is varied. We also apply our new measures to empirical data from
semiconductor lasers and show that they are able to anticipate the polarization
switchings, thus providing early warning signals of abrupt transitions.Comment: 18 pages, 9 figures, to appear in New Journal of Physic
Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
Entanglement measures such as the entanglement entropy have become an
indispensable tool to identify the fundamental character of ground states of
interacting quantum many-body systems. For systems of interacting spin or
bosonic degrees of freedom much recent progress has been made not only in the
analytical description of their respective entanglement entropies but also in
their numerical classification. Systems of interacting fermionic degrees of
freedom however have proved to be more difficult to control, in particular with
regard to the numerical understanding of their entanglement properties. Here we
report a generalization of the replica technique for the calculation of Renyi
entropies to the framework of determinantal Quantum Monte Carlo simulations --
the numerical method of choice for unbiased, large-scale simulations of
interacting fermionic systems. We demonstrate the strength of this approach
over a recent alternative proposal based on a decomposition in free fermion
Green's functions by studying the entanglement entropy of one-dimensional
Hubbard systems both at zero and finite temperatures.Comment: 11 pages, 10 figure
Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching
Motivated by recent understandings in the stochastic natures of gene
expression, biochemical signaling, and spontaneous reversible epigenetic
switchings, we study a simple deterministic cell population dynamics in which
subpopulations grow with different rates and individual cells can
bi-directionally switch between a small number of different epigenetic
phenotypes. Two theories in the past, the population dynamics and
thermodynamics of master equations, separatedly defined two important concepts
in mathematical terms: the {\em fitness} in the former and the (non-adiabatic)
{\em entropy production} in the latter. Both play important roles in the
evolution of the cell population dynamics. The switching sustains the
variations among the subpopulation growth thus continuous natural selection. As
a form of Price's equation, the fitness increases with () natural selection
through variations and a positive covariance between the per capita
growth and switching, which represents a Lamarchian-like behavior. A negative
covariance balances the natural selection in a fitness steady state | "the red
queen" scenario. At the same time the growth keeps the proportions of
subpopulations away from the "intrinsic" switching equilibrium of individual
cells, thus leads to a continous entropy production. A covariance, between the
per capita growth rate and the "chemical potential" of subpopulation,
counter-acts the entropy production. Analytical results are obtained for the
limiting cases of growth dominating switching and vice versa.Comment: 16 page
Computational Capacity and Energy Consumption of Complex Resistive Switch Networks
Resistive switches are a class of emerging nanoelectronics devices that
exhibit a wide variety of switching characteristics closely resembling
behaviors of biological synapses. Assembled into random networks, such
resistive switches produce emerging behaviors far more complex than that of
individual devices. This was previously demonstrated in simulations that
exploit information processing within these random networks to solve tasks that
require nonlinear computation as well as memory. Physical assemblies of such
networks manifest complex spatial structures and basic processing capabilities
often related to biologically-inspired computing. We model and simulate random
resistive switch networks and analyze their computational capacities. We
provide a detailed discussion of the relevant design parameters and establish
the link to the physical assemblies by relating the modeling parameters to
physical parameters. More globally connected networks and an increased network
switching activity are means to increase the computational capacity linearly at
the expense of exponentially growing energy consumption. We discuss a new
modular approach that exhibits higher computational capacities and energy
consumption growing linearly with the number of networks used. The results show
how to optimize the trade-off between computational capacity and energy
efficiency and are relevant for the design and fabrication of novel computing
architectures that harness random assemblies of emerging nanodevices
Quantum dynamics, dissipation, and asymmetry effects in quantum dot arrays
We study the role of dissipation and structural defects on the time evolution
of quantum dot arrays with mobile charges under external driving fields. These
structures, proposed as quantum dot cellular automata, exhibit interesting
quantum dynamics which we describe in terms of equations of motion for the
density matrix. Using an open system approach, we study the role of asymmetries
and the microscopic electron-phonon interaction on the general dynamical
behavior of the charge distribution (polarization) of such systems. We find
that the system response to the driving field is improved at low temperatures
(and/or weak phonon coupling), before deteriorating as temperature and
asymmetry increase. In addition to the study of the time evolution of
polarization, we explore the linear entropy of the system in order to gain
further insights into the competition between coherent evolution and
dissipative processes.Comment: 11pages,9 figures(eps), submitted to PR
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