Nonequilibrium Phenomena and Anomalous Behavior

Commun. Theor. Phys. 62 (2014) 631–633

Vol. 62, No. 4, October 1, 2014

Bibliography on Small Systems: Nonequilibrium Phenomena and Anomalous Behavior The workshop and satellite conference held in July 2013 at the Kavli Institute for Theoretical Physics China (KITPC) of the Chinese Academy of Sciences (CAS) brought together experts of a variety of diÆerent fields, and constituted a unique opportunity to share ideas and breed new ones in a strongly interdisciplinary fashion. At the same time, the breadth of the scope of these two meetings was so wide that the need for a collection of reference books and papers was pointed out, in order to help the interested professionals, as well as graduate students, both to tackle the technically advanced issues and to bridge the gaps, necessarily present in each other’s background. Therefore, we invited some of the participants to produce a bibliography containing the most relevant works in their own fields, and to complement this bibliography with a short explanation of the content of those books and papers. We are thus very grateful to Igor Goychuk, David Lacoste, Annick Lesne, Andrea Puglisi, Hong Qian and Hugo Touchette for having accepted our invitation and for having produced what we consider a very useful tool for all those who want to learn or to understand more deeply the current theories concerning small and nonequilibrium systems. LIU Fei, Lamberto Rondoni, TANG Lei-Han, ZHOU Hai-Jun, and WANG Yan-Ting Bibliography provided by Igor Goychuk: I. Goychuk, Viscoelastic subdiÆusion: from anomalous to normal , Phys. Rev. E 80 (2009) 046125, selected for Virtual Journal of Biological Physics Research 18, Issue 9 (1 November 2009). Seminal paper on viscoelastic subdiÆusion and rate processes in double well and washboard potentials within a well-founded non-Markovian Generalized Langevin Equation approach and a corresponding multi-dimensional Markovian embedding. A number of new and correct results are obtained for the first time, refuting earlier incorrect approaches to this di±cult problem. It contains also the first discussion of ergodicity of viscoelastic subdiÆusion in washboard potentials. I. Goychuk, Viscoelastic SubdiÆusion: Generalized Langevin Equation Approach, Adv. Chem. Phys. 150 (2012) 187–253. Review on viscoelastic subdiÆusion in multistable potentials. Apart from general methodological importance, it contains also new important results, in particular, on the universality class of viscoelastic subdiÆusion and transport in washboard potentials. This is also the second paper on anomalous Brownian motors and ratchets based on viscoelastic subdiÆusion pioneered earlier by this author. I. Goychuk and P. Hanggi, Quantum dynamics in strong fluctuating fields, Adv. Phys. 54 (2005) 525–584. Review on dissipative quantum dynamics in strong external fields. Apart from general methodological importance, it reviews in particular also the earlier works (1998–2000) on quantum dissipative ratchets/rectifiers and pumps pioneered by these authors. G. Schmid, I. Goychuk, and P. Hanggi, Stochastic resonance as a collective property of ion channel assemblies, Europhys. Lett. 56 (2001) 22–28. This is a seminal paper on mesoscopic noise eÆects for stochastic and coherence resonances in excitable neuronal systems due to a finite number of ion channels. Bibliography provided by David Lacoste U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75 (2012) 126001. This is a review about stochastic thermodynamics, which is defined as a framework for extending the notions about classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles”. D. Andrieux, P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud, and A Petrosyan, Thermodynamic time asymmetry in non-equilibrium fluctuations, J. Stat. Mech. (2008) P01002. In this paper the average dissipation produced in an experiment based on a driven brownian colloidal particle is estimated from the temporal asymmetry of the recorded fluctuations. In this work, the exact known value of the dissipation is recovered from the diÆerence of temporal disorder present in the fluctuations of the forward and of the backward process. R. Kawai, J. M. R. Parrondo, and C. Van den Broeck, Dissipation: The Phase-Space Perspective, Phys. Rev. Lett. 98 (2007) 080602. In this paper, it is shown that the average dissipation can be expressed as the relative entropy between the phase-space density of the system measured at the same intermediate point in time for the forward and the backward process. In other words, the dissipation is intimately linked to the notion of an arrow of time.

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S. Muy, A. Kundu, and D. Lacoste, Non-invasive estimation of dissipation from non-equilibrium fluctuations in chemical reactions, J. Chem. Phys. 139 (2013) 124109. In this paper, it is shown how to extract an estimate of the entropy production from a su±ciently long time series of stationary fluctuations of chemical reactions. This method, which is based on recent work on fluctuation theorems, is direct, non-invasive, does not require any knowledge about the underlying dynamics and is applicable even when only partial information is available. Bibliography provided by Annick Lesne: J.B. Imbert, A. Lesne, and J.M. Victor, On the distribution of the order parameter of the coil-globule transition, Phys. Rev. E 56 (1997) 5630–5647. This paper presents a framework to describe conformational transitions of a finite-size linear polymer: studying the order parameter distribution and its dependence on the polymer size allows evidencing both the nature of the transition (focusing on the example of the coil-globule transition and its tri-critical nature) and the scaling laws it satisfies. H. Schiessel, The physics of chromatin, J. Phys.: Condens. Matter 15 (2003) R699–R774. This seminal review presents the advances that have been made in understanding the physical properties of the chromatin (the intermediary level of organization between DNA and chromosome). It underlines the importance of taking into account these physical properties for understanding DNA folding into a chromatin fiber, capable at the same time to achieve a high degree of DNA compaction within the cell nucleus and to preserve the accessibility to genes and regulatory sequences required for their expression. A. Lesne and J.M. Victor, Chromatin fiber functional organization: some plausible models, Eur. Phys. J. E 19 (2006) 279–290. This paper proposes some integrated scenarios in which the interplay between the physical features of the chromatin fiber organization and the action of specific biological factors could achieve genomic functions. J. Dekker, K. Rippe, M. Dekker, and N. Kleckner, Capturing Chromosome Conformation, Science 295 (2002) 1306–1311. This paper presents the recent experimental technologies for in vivo measurement of pairwise contacts (in 3D space) between genomic loci. It shows that polymer models of the chromatin fiber can be used for making sense out of these data, in particular for deriving quantitative information on some chromatin features such as its compaction and its flexibility Bibliography provided by Andrea Puglisi: K. Sekimoto, Stochastic energetics, Lecture Notes in Physics, Springer Verlag, Berlin (2010). This book represents a clear introduction to the most recent topics of nonequilibrium statistical physics, especially fluctuations of heat and work. It has the merit of being suitable not only for experienced researchers, but also for graduate students. R. Chetrite and K. Gawedzki, Fluctuation Relations for DiÆusion Processes, Commun. Math. Phys. 282 (2008) 469–518. This paper is an updated review on the topics of fluctuation relations for diÆusion processes, written from the perspective of mathematical physics. In view of the great generality of fluctuation relations, a formal approach which unveils the mathematical structure of these relations is important. U. M. Bettolo Marconi, A. Puglisi, L. Rondoni and A. Vulpiani, Fluctuation-Dissipation: Response Theory in Statistical Physics, Phys. Reports 461 (2008) 111. This paper is a review on response theory in classical statistical physics, going from the historical results valid at equilibrium up to the most recent and still debated results for nonequilibrium systems. It covers many applications (turbulence, granular systems, geophysics) and also includes a detailed discussion of fluctuation relations. A. Gnoli, et al., Brownian Ratchet in a Thermal Bath Driven by Coulomb Friction, Phys. Rev. Lett. 110 (2013) 120601. This paper reports recent progresses in the theory of Brownian ratchets (nonequilibrium stochastic processes where unbiased fluctuations are ”rectified”). Remarkably, the paper also includes experimental verifications of the theoretical predictions. Coulomb non-linear friction plays a fundamental role in the theory and in the experiments. Bibliography provided by Hong Qian: D. Chowdhury, Stochastic mechano-chemical kinetics of molecular motors: A multidisciplinary enterprise from a physicists perspective, Phys. Reports 529 (2013) 1–197. This is an up-to-date, authoritative review of the enormous literature on molecular motor. Since mid-1990s, the field of molecular motor has been a very active area of research at the junction between several interdisciplinary areas: biophysics that includes single-molecule experiments and modeling, in statistical physics it serves as a concrete example of open, chemically driven systems exhibiting nonequilibrium steady state with positive entropy production, and for applied mathematics it provides systems of irreversible stochastic

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processes and coupled diÆusion with Markov switching. It reports a great deal of new development since the earlier reviews by Julicher, et al. (Rev. Mod. Phys., 1997) and Reiman (Phys. Rep., 2002), and has a much broader scope than a recent one by Kolomeisky and Fisher (Ann. Rev. Phys. Chem., 2007). J. Goutsias and G. Jenkinson, Markovian dynamics on complex reaction networks, Phys. Reports 529 (2013) 199– 264; H. Qian and S.C. Kou, Statistics and related topics in single-molecule biophysics, Ann. Rev. Stat. Application 1 (2014) 465–492. Biophysics at the level of individual macromolecules, e.g., proteins and DNA in aqueous solution, can be rigorously represented and characterized in terms of stochastic processes, either Markovian or processes with long correlations such as fractional Brownian motion. Recent progress in single-molecule biophysics as an experimental subject has generated a large amount of data that should be interested by statisticians and applied probabilities. The paper suggests this type of data is particularly important to quantitative sciences since it is one of the few areas where both mechanistically derived stochastic-process models and statistics analysis of data can meet. The review shows how the study of single-molecules is a natural continuation of earlier work by Smoluchowski, Einstein, Langevin, Kac, and provides many new challenges and opportunities. It argues that many key chemical concepts are actually statistical in nature. H. Qian, Cooperativity in cellular biochemical processes: Noise-enhanced sensitivity, fluctuating enzyme, bistability with nonlinear feedback, and other mechanisms for sigmoidal responses, Ann. Rev. Biophys. 41 (2012) 179–204. Focusing on cooperative sharp transitions and its relation to bistability, this review attempts to bridge molecular biophysics which studies individual macromolecules and the emerging biophysics of single cells. Both can be represented in terms of nonlinear, stochastic dynamical systems with individuals exhibiting random behavior. The review uses a language familiar to molecular biophysicists and presents the new stochastic biophysical theory and models of single cells as a “biochemical reaction system”. The dynamic attractors in the latter are to be understood as stable phenotypes in cell biology; stochastic jumps between attractors, either spontaneous or induced by changing environment, are to be understood as phenotype switching. Stationary fluctuations in a biochemical reaction system are nonequilibrium; thus they contain informations and chemical energy, which can be utilized to drive, or perform, biological functions. Bibliography provided by Hugo Touchette: R.S. Ellis, An overview of the theory of large deviations and applications to statistical mechanics, Scandinavian Actuarial J. 1 (1995) 97–142. Very good and very readable (for physicists) introduction to large deviation theory as applied to equilibrium systems, conveying all the basic ideas without an excess of mathematical notations. Not easy to find, but Ellis has a PDF file available on his website. R. Graham, Macroscopic potentials, bifurcations and noise in dissipative systems, in Noise in Nonlinear Dynamical Systems, Vol. 1 , F. Moss and P. V. E. McClintock, eds., Cambridge University Press, Cambridge (1989) pp. 225–278. The best paper, in my opinion, for learning about small-noise large deviations of dynamical systems perturbed by noise. It gives all the basic ideas and the physics behind the rigorous theory known in mathematics as the Freidlin-Wentzell theory. The paper also contains many results that have been derived and re-derived in the so-called hydrodynamic fluctuation theory. F. den Hollander, Large Deviations, Fields Institute Monograph, AMS, Providence (2000). Most readable textbook on large deviations and some applications in applied mathematics and physics. The balance between notations and mathematics, on the one hand, and the meaning and interpretation of large deviation results, on the other, is ideal. H. Touchette, The large deviation approach to statistical mechanics, Phys. Reports 478 (2009) 1–69. http://dx.doi.org/ 10.1016/j.physrep.2009.05.002 Something more up to date (with all modesty) on large deviation theory and its applications in statistical physics, especially on nonequilibrium systems