64,037 research outputs found
Boundedness in Complex Systems: New Approach to Power Law Distributions
A new approach to complex systems aimed to resolve their paradoxes is
proposed. Yet, the major inference is the prohibition of informational
perpetuum mobileComment: 11 p. 2 fi
Is Semantics Physical?!
It is demonstrated that under the hypothesis of boundedness, the semantics
appears as a property of spontaneous physical processes. It turns that both
semantic structure and semantic meaning have their own physical agents each of
which is represented trough generic for the state space property. The
boundedness sets an exclusive two-fold representation of a semantic unit: as a
specific sequence of letters and as a performance of a specific engine so that
their interplay serves as grounds for building a multi-layer hierarchy of
semantic structures. It is established that in this setting the semantics
admits both non-extensivity, permutation sensitivity and Zipf`s law. The
robustness of the hierarchical organization of semantic structures is
maintained by new generic form of non-local feedback that appears as a result
of the necessary for sustaining boundeness matter wave emitting.Comment: 11 pp, no fi
Self-Organization and Finite Velocity of Transmitting Substance and Energy through Space-Time
The idea that the velocity of transmitting substance/energy trough space-time
is to be bounded is a fundamental concept in the science. To the most surprise,
it turns out that it is not always met. We demonstrate that the existing
approaches to the self-organization, another major concept in the science, let
the velocity of transmitting substance to be arbitrary. Further we prove that
only the boundedness of the velocity is not enough to ensure the
self-organization. That is why we develop radically novel approach to the
macroscopic evolution that not only reconciles the self-organization and the
velocity ansatz but in addition gives physically credible basis to phenomena
like Feigenbaum cascade and fluctuation-assisted bifurcations.Comment: 10 pages, no figure
Metastability, Spectra, and Eigencurrents of the Lennard-Jones-38 Network
We develop computational tools for spectral analysis of stochastic networks
representing energy landscapes of atomic and molecular clusters. Physical
meaning and some properties of eigenvalues, left and right eigenvectors, and
eigencurrents are discussed. We propose an approach to compute a collection of
eigenpairs and corresponding eigencurrents describing the most important
relaxation processes taking place in the system on its way to the equilibrium.
It is suitable for large and complex stochastic networks where pairwise
transition rates, given by the Arrhenius law, vary by orders of magnitude. The
proposed methodology is applied to the network representing the
Lennard-Jones-38 cluster created by Wales's group. Its energy landscape has a
double funnel structure with a deep and narrow face-centered cubic funnel and a
shallower and wider icosahedral funnel. Contrary to the expectations, there is
no appreciable spectral gap separating the eigenvalue corresponding to the
escape from the icosahedral funnel. We provide a detailed description of the
escape process from the icosahedral funnel using the eigencurrent and
demonstrate a superexponential growth of the corresponding eigenvalue. The
proposed spectral approach is compared to the methodology of the Transition
Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is
metastable from the points of view of a mathematician and a chemical physicist,
and make a connection with experimental works.Comment: 24 pages, 10 figure
Stochastic Thermodynamics and Dynamics: A Tail of Unexpected
The problem of the insensitivity of the macroscopic behavior of any
thermodynamical system to partitioning generates a bias between the
reproducibility of its macroscopic behavior viewed as the simplest form of
causality and its long-term stability. The overcoming of this controversy goes
through certain modification of the dynamics that involves self-assembling of
the boundary conditions. Subsequently the proposed approach justifies parity
between the increase and the decrease of the entropy which provides the ground
for holistic understanding of the thermodynamical systems through launching
their ability to transmit and create information that is sensitive to coherent
functioning of self-assembled logical landscapes. The obtained sensitivity
gives the advantage of this new approach compared to that of Shannon. According
to his definition, the information depends only on the overall probability for
realization of a given state(s) and thus it does not distinguish between
functionally different states provided the overall probability for the
realization of each of them is equal.Comment: 7 pages, novel approach to the securiiy of encrypting that comes out
from the considerations in the paper is proposed in the revised versio
Computing the Asymptotic Spectrum for Networks Representing Energy Landscapes using the Minimal Spanning Tree
The concept of metastability has caused a lot of interest in recent years.
The spectral decomposition of the generator matrix of a stochastic network
exposes all of the transition processes in the system. The assumption of the
existence of a low lying group of eigenvalues separated by a spectral gap,
leading to factorization of the dynamics, has become a popular theme. We
consider stochastic networks representing potential energy landscapes where the
states and the edges correspond to local minima and transition states
respectively, and the pairwise transition rates are given by the Arrhenuis
formula. Using the minimal spanning tree, we construct the asymptotics for
eigenvalues and eigenvectors of the generator matrix starting from the low
lying group. This construction gives rise to an efficient algorithm for
computing the asymptotic spectrum suitable for large and complex networks. We
apply it to Wales's Lennard-Jones-38 network with 71887 states and 119853 edges
where the underlying potential energy landscape has a double-funnel structure.
Our results demonstrate that the concept of metastability should be applied
with care to this system. In particular, for the full network, there is no
significant spectral gap separating the eigenvalue corresponding to the exit
from the wider and shallower icosahedral funnel at any reasonable temperature
range.Comment: Submitted to Journal Networks and Heterogeneous Media on Feb. 25,
2014, 36 pages, 14 figure
Sustainable Evolution in an Ever-Changing Environment: General Characterization
A complex interplay between the academic issue about generalization of the
thermodynamics and the practical matter about setting standards for a
sustainable evolution of both tailored devices and natural systems is
considered. It is established that the measure for a sustainable evolution in
an ever-changing environment appears as a Boltzmann-Gibbs weight. At the same
time, this measure performs as a local thermodynamical potential which, at the
expense of being released from the condition of entropy maximization, serves as
grounds for a fundamental development of the idea of banning perpetuum mobile.
It is proven that the best efficiency of each engine that operates reversibly
never exceeds the efficiency of corresponding Carnot heat engine where the
engine is free from necessity of a physical coupling to two heat reservoirs.Comment: 10 pages, 1 figur
Size-Independent Non-Equilibrium Fluctuations
A local quantum phenomenon that gives rise to generic for all surface
reactions macroscopic fluctuations is studied. The issue is viewed with respect
to the necessary conditions for a long-term stable evolution of any natural and
artificial system. It is shown that global coupling of the local fluctuations
is necessary for providing a long-term stability of the system. A successful
coupling mechanism is achieved on the grounds of new assumptions about the
Hamiltonian response to certain perturbations. The coupling mechanism acts
towards a global synchronisation, i.e. to a coherent response of the excited
species to any further perturbation. It is proven that the synchronisation is a
scale-free process that has universal properties, e.g. it is insensitive to the
chemical identity of the reacting species and to the particularities of the
surface reaction. Its hallmark is that the global adsorption rate exhibits
permanent temporal variations whose amplitude is independent of the system
size.
The presence of these fluctuations fundamentally changes the temporal
behavior of the system, namely it becomes pulse-like both on the quantum and
the macro-level. The pulse-like behavior gives rise to a persistent continuous
band at the quantum spectra whose major properties are: (I) it does not
correspond to any real radiation; (ii) its presence is insensitive to the
particularities of the system and the incident radiation; (iii) its shape and
the infrared edge are typical for the -type noise. These properties give rise
to its name: alias -type noise.Comment: 22 pages, major revisio
Coarse-Grained Structure of a Physical (Strange) Attractor. Analytical Solution
The structure of the physical and strange attractors is inherently associated
with the boundedness of fluctuations. The idea behind the boundedness is that a
stable long-term evolution of any natural and engineered system is possible if
and only if the fluctuations that the system exerts are bounded so that the
system permanently stays within its thresholds of stability. It has been
established that the asymptotic structure of the physical and strange
attractors is identical. Now it is found out that though the non-asymptotic
behavior is universal it can be very different, namely: on coarse-graining the
physical attractors can exhibit a variety of behavior while the strange
attractors always have hyperuniversal properties. Yet, under certain levels of
coarse-graining both physical and strange attractors match non-asymptotically a
variety of noise type behavior.Comment: 7 pages, presented at 5-th Int. Conference "Symmetry in Non-Linear
Mathematical Physics", 23-29 June 2003, Kie
Integrated Harnack inequalities on Lie groups
We show that the logarithmic derivatives of the convolution heat kernels on a
uni-modular Lie group are exponentially integrable. This result is then used to
prove an "integrated" Harnack inequality for these heat kernels. It is shown
that this integrated Harnack inequality is equivalent to a version of Wang's
Harnack inequality. (A key feature of all of these inequalities is that they
are dimension independent.) Finally, we show these inequalities imply
quasi-invariance properties of heat kernel measures for two classes of infinite
dimensional "Lie" groups.Comment: 41 pages A section added where we show that this integrated Harnack
inequality is equivalent to a version of Wang's Harnack inequality. New
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