2014年, 第62卷, 第04期　
刊出日期：2014-10-01

  

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Small Systems: Nonequilibrium Phenomena and Anomalous Behavior
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  Preface to Special Issue on Small Systems：Nonequilibrium Phenomena and Anomalous Behavior

  LIU Fei, Lamberto Rondoni, TANG Lei-Han, WANG Yan-Ting, ZHOU Hai-Jun

  理论物理通讯. 2014, 62(04): 0-0.

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  Exact Solutions and Their Asymptotic Behaviors for the Averaged Generalized Fractional Elastic Models

  李灿, 邓伟华, 沈晓芹

  理论物理通讯. 2014, 62(04): 443-450.

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  The generalized fractional elastic models govern the stochastic motion of several many-body systems, e.g., polymers, membranes, and growing interfaces. This paper focuses on the exact formulations and their asymptotic behaviors of the average of the solutions of the generalized fractional elastic models. So we directly analyze the Cauchy problem of the averaged generalized elastic model involving time fractional derivative and the convolution integral of a radially symmetric friction kernel with space fractional Laplacian.
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  What Does Dynamical Systems Theory Teach Us about Fluids?

  Hadrien Bosetti, Harald A. Posch

  理论物理通讯. 2014, 62(04): 451-468.

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  We use molecular dynamics simulations to compute the Lyapunov spectra of many-particle systems resembling simple fluids in thermal equilibrium and in non-equilibrium stationary states. Here we review some of the most interesting results and point to open questions.
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  On the Foundations of Statistical Mechanics：Ergodicity, Many Degrees of Freedom and Inference

  Sergio Chibbaro, Lamberto Rondoni, Angelo Vulpiani

  理论物理通讯. 2014, 62(04): 469-475.

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  We review the main aspects of the foundations of statistical mechanics. In particular we explain why many degrees of freedom are necessary, while chaos (in the sense of positive Lyapunov exponents) is only marginally relevant, for the emergence of statistical laws in macroscopic systems.
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  Theoretical Analysis of the Fluctuation Theorem Applied to Electric Circuits

  Charlotte F. Petersen, Elmars Krausz, Denis J. Evans, Stephen R. Williams

  理论物理通讯. 2014, 62(04): 476-484.

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  We carry out a theoretical analysis of the fluctuations in the Johnson-Nyquist noise in an RC electric circuit being driven by a non-ideal constant current source. Using the appropriate Langevin equation, we derive the fluctuation theorem for the system. This analysis exhibits some interesting features. Firstly, the average of the dissipation function is not necessarily just an instantaneous entropy production, i.e. the work being done on the circuit by the external power source divided by the ambient temperature. Secondly, by appropriate selection of the values for the circuit components, the transient response of the system can be made identical to the nonequilibrium steady state response. In the limit of an ideal current source, the average of the dissipation function reduces to the entropy production. Our analysis accurately reproduces published experimental results.
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  Solving for the Fixed Points of 3-Cycle in the Logistic Map and Toward Realizing Chaos by the Theorems of Sharkovskii and Li-Yorke

  M. Howard Lee

  理论物理通讯. 2014, 62(04): 485-496.

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  Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obtained analytically by solving a sextic equation. At one parametric value, a fixed-point spectrum, resulted from the Sharkovskii limit, helps to realize chaos in the sense of Li and Yorke.
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  Life and Death of Stationary Linear Response in Anomalous Continuous Time Random Walk Dynamics

  Igor Goychuk

  理论物理通讯. 2014, 62(04): 497-504.

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  Linear theory of stationary response in systems at thermal equilibrium requires to find equilibrium correlation function of unperturbed responding system. Studies of the response of the systems exhibiting anomalously slow dynamics are often based on the continuous time random walk description (CTRW) with divergent mean waiting times. The bulk of the literature on anomalous response contains linear response functions like one by Cole-Cole calculated from such a CTRW theory and applied to systems at thermal equilibrium. Here we show within a fairly simple and general model that for the systems with divergent mean waiting times the stationary response at thermal equilibrium is absent, in accordance with some recent studies. The absence of such stationary response (or dying to zero non-stationary response in aging experiments) would confirm CTRW with divergent mean waiting times as underlying physical relaxation mechanism, but reject it otherwise. We show that the absence of stationary response is closely related to the breaking of ergodicity of the corresponding dynamical variable. As an important new result, we derive a generalized Cole-Cole response within ergodic CTRW dynamics with finite waiting time. Moreover, we provide a physically reasonable explanation of the origin and wide presence of 1/f noise in condensed matter for ergodic dynamics close to normal, rather than strongly deviating.
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  Coulomb Friction Driving Brownian Motors

  Alessandro Manacorda, Andrea Puglisi, Alessandro Sarracino

  理论物理通讯. 2014, 62(04): 505-513.

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  We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation (linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein-Kramers equation. In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.
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  Scaling Properties of Field-Induced Superdiffusion in Continuous Time Random Walks

  R. Burioni, G. Gradenigo, A. Sarracino, A. Vezzani, A. Vulpiani

  理论物理通讯. 2014, 62(04): 514-520.

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  We consider a broad class of Continuous Time Random Walks (CTRW) with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Lévy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
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  Diffusion in the Lorentz Gas

  Carl P. Dettmann

  理论物理通讯. 2014, 62(04): 521-540.

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  The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises recent results, including periodic and aperiodic models, finite and infinite horizon, external fields, smooth or polygonal obstacles, and in the Boltzmann-Grad limit. New results are given for several moving particles and for obstacles with flat points. Finally, a variety of applications are presented.
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  Sieving of H₂ and D₂ Through End-to-End Nanotubes

  Devagnik Dasgupta, Debra J. Searles, Lamberto Rondoni, Stefano Bernardi

  理论物理通讯. 2014, 62(04): 541-549.

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  We study the quantum molecular sieving of H₂ and D₂ through two nanotubes placed end-to-end. An analytic treatment, assuming that the particles have classical motion along the axis of the nanotube and are confined in a potential well in the radial direction, is considered. Using this idealistic model, and under certain conditions, it is found that this device can act as a complete sieve, allowing chemically pure deuterium to be isolated from an isotope mixture. We also consider a more realistic model of two carbon nanotubes and carry out molecular dynamics simulations using a Feynman-Hibbs potential to model the quantum effects on the dynamics of H₂ and D₂. Sieving is also observed in this case, but is caused by a different process.
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  Small Open Chemical Systems Theory：Its Implications to Darwinian Evolution Dynamics, Complex Self-Organization and Beyond

  QIAN Hong

  理论物理通讯. 2014, 62(04): 550-554.

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  The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time deterministic nonlinear dynamics, and long-time evolutionary behavior with exponentially distributed rare events, discrete jumps among punctuated equilibria, and catastrophe.
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  Energy and Heat Fluctuations in a Temperature Quench

  M. Zannetti, F. Corberi, G. Gonnella, A. Piscitelli

  理论物理通讯. 2014, 62(04): 555-570.

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  Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large N model quenched below the critical temperature T_C. The main finding is that fluctuations exceeding a critical threshold do condense. Though driven by a mechanism similar to that of Bose-Einstein condensation, this phenomenon is an out-of-equilibrium feature produced by the breaking of energy equipartition occurring in the transient regime. The dynamical nature of the transition is illustrated by phase diagrams extending in the time direction.
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  Generalized Integral Fluctuation Relation with Feedback Control for Diffusion Processes

  柳飞, 谢洪城, 卢志悦

  理论物理通讯. 2014, 62(04): 571-578.

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  We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation. This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.
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  One-Dimensional Steady Transport by Molecular Dynamics Simulation：Non-Boltzmann Position Distribution and Non-Arrhenius Dynamical Behavior

  石锐, 王延颋

  理论物理通讯. 2014, 62(04): 579-588.

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  A non-equilibrium steady state can be characterized by a nonzero but stationary flux driven by a static external force. Under a weak external force, the drift velocity is difficult to detect because the drift motion is feeble and submerged in the intense thermal diffusion. In this article, we employ an accurate method in molecular dynamics simulation to determine the drift velocity of a particle driven by a weak external force in a one-dimensional periodic potential. With the calculated drift velocity, we found that the mobility and diffusion of the particle obey the Einstein relation, whereas their temperature dependences deviate from the Arrhenius law. A microscopic hopping mechanism was proposed to explain the non-Arrhenius behavior. Moreover, the position distribution of the particle in the potential well was found to deviate from the Boltzmann equation in a non-equilibrium steady state. The non-Boltzmann behavior may be attributed to the thermostat which introduces an effective "viscous" drag opposite to the drift direction of the particle.
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  Coefficient of Performance at Maximum χ-Criterion for Feynman Ratchet as a Refrigerator

  盛世奇, 杨盼, 涂展春

  理论物理通讯. 2014, 62(04): 589-595.

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  The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tomás et al., Phys. Rev. E 85 (2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χ is investigated.
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  Kinetic Density Functional Theory：A Microscopic Approach to Fluid Mechanics

  Umberto Marini Bettolo Marconi, Simone Melchionna

  理论物理通讯. 2014, 62(04): 596-606.

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  In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme confinement, such as nanopores, nanodevices, etc. The approach obtained by combining kinetic and density functional methods is microscopic, fully self-consistent and allows to determine both configurational and flow properties of dense fluids. The theory predicts the correct hydrodynamic behavior and provides a practical and numerical tool to determine how the transport properties are modified when the length scales of the confining channels are comparable with the size of the molecules. The applications range from the dynamics of simple fluids under confinement, to that of neutral binary mixtures and electrolytes where the theory in the limit of slow gradients reproduces the known phenomenological equations such as the Planck-Nernst-Poisson and the Smolochowski equations. The approach here illustrated allows for fast numerical solution of the evolution equations for the one-particle phase-space distributions by means of the weighted density lattice Boltzmann method and is particularly useful when one considers flows in complex geometries.
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  Finite-Size Conformational Transitions：A Unifying Concept Underlying Chromosome Dynamics

  Bertrand R. Caré, Pascal Carrivain, Thierry Forné, Jean-Marc Victor, Annick Lesne

  理论物理通讯. 2014, 62(04): 607-616.

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  Investigating average thermodynamic quantities is not sufficient to understand conformational transitions of a finite-size polymer. We propose that such transitions are better described in terms of the probability distribution of some finite-size order parameter, and the evolution of this distribution as a control parameter varies. We demonstrate this claim for the coil-globule transition of a linear polymer and its mapping onto a two-state model. In a biological context, polymer models delineate the physical constraints experienced by the genome at different levels of organization, from DNA to chromatin to chromosome. We apply our finite-size approach to the formation of plectonemes in a DNA segment submitted to an applied torque and the ensuing helix-coil transition that can be numerically observed, with a coexistence of the helix and coil states in a range of parameters. Polymer models are also essential to analyze recent in vivo experiments providing the frequency of pairwise contacts between genomic loci. The probability distribution of these contacts yields quantitative information on the conformational fluctuations of chromosome regions. The changes observed in the shape of the distribution when the cell type or the physiological conditions vary may reveal an epigenetic modulation of the conformational constraints experienced by the chromosomes.
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  Statistical Mechanics Analysis of ATP Binding to a Multisubunit Enzyme

  张云新

  理论物理通讯. 2014, 62(04): 617-621.

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  Due to inter-subunit communication, multisubunit enzymes usually hydrolyze ATP in a concerted fashion. However, so far the principle of this process remains poorly understood. In this study, from the viewpoint of statistical mechanics, a simple model is presented. In this model, we assume that the binding of ATP will change the potential of the corresponding enzyme subunit, and the degree of this change depends on the state of its adjacent subunits. The probability of enzyme in a given state satisfies the Boltzmann's distribution. Although it looks much simple, this model can fit the recent experimental data of chaperonin TRiC/CCT well. From this model, the dominant state of TRiC/CCT can be obtained. This study provide a new way to understand biophysical processe by statistical mechanics analysis.
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  Effect of a Local Source or Sink of Inhibitor on Turing Patterns

  P. Dziekan, L. Signon, B. Nowakowski, A. Lemarchand

  理论物理通讯. 2014, 62(04): 622-630.

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  We investigate a reaction-diffusion model in which a Turing pattern develops and reproduces the formation of periodic segments behind a propagating chemical wave front. The chemical scheme involves two species known as activator and inhibitor. The model can be used to mimic the formation of prevertebrae during the early development of vertebrate embryo. Deterministic and stochastic analyses of the reaction-diffusion processes are performed for two typical sets of parameter values, far from and close to the Turing bifurcation. The effects of a local source or sink of inhibitor on the growing structure are studied and successfully compared with experiments performed on chick embryos. We show that fluctuations may lead to the formation of additional prevertebra.
Interdisciplinary Physics and Related Areas of Science and Technology
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  Bibliography on Small Systems：Nonequilibrium Phenomena and Anomalous Behavior

  LIU Fei, Lamberto Rondoni, TANG Lei-Han, ZHOU Hai-Jun, WANG Yan-Ting

  理论物理通讯. 2014, 62(04): 631-633.

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