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 abstrac