From space-time chaos to stochastic thermodynamics

We summarize the results of several experiments that show the evolution of some scientific interests and goals of the statistical and nonlinear physics community in the last 40 years. Specifically, we present how the ideas of extending concepts of equilibrium statistical physics to out-of-equilibrium physics have been developed to characterize various phenomena such as, for example, transition to space-time chaos and glass aging. We then discuss the applications of this out-of-equilibrium thermodynamics to microsystems driven out of equilibrium either by external forces or by temperature gradients. We show that in these systems thermal fluctuations play a role and that all thermodynamics quantities, such as work, heat, and entropy fluctuate. We recall general concepts such as fluctuation theorems and fluctuation dissipation relations used to characterize the statistical properties of these small systems. We describe experiments where all these concepts have been applied and tested with high accuracy. Finally, we show how these theoretical concepts and the experiments allowed us to improve our knowledge on the connection between information and thermodynamics.     

Quantum thermodynamics

Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations and with the full inclusion of quantum effects. Fuelled by experimental advances and the potential of future nanoscale applications, this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of ‘work’ to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.     

Thermomechanics of DNA: theory of thermal stability under load

A theory for thermomechanical behavior of homogeneous DNA at thermal equilibrium predicts critical temperatures for denaturation under torque and stretch, phase diagrams for stable B-DNA, supercoiling, optimally stable torque, and the overstretching transition as force-induced DNA melting. Agreement with available single molecule manipulation experiments is excellent.     

An introduction to the physics of the bacterial flagellar motor: a nanoscale rotary electric motor

Biological molecular motors show us how directed motion can be generated by nanometre-scale devices that work at the energy scale of the thermal bath. Direct and indirect observations of functioning single molecule motors allow us to see fundamental processes of statistical physics unfolding in microscopic detail at room temperature, something that was unimaginable only a few decades ago. In this review, we introduce molecular motors and the physics relevant to their mechanisms before focusing on our recent experiments on the bacterial flagellar motor, the rotary device responsible for bacterial locomotion.     

Deterministic patterns of noise and the control of chaos

Real systems in physics, chemistry and biology are always subject to fluctuations that change qualitatively the systems' dynamics. In particular, rare large fluctuations are responsible for the nucleation at phase transitions, mutations in DNA sequences, protein transport in cells and failure of electronic devices. In many cases of practical interest systems are away from thermal equilibrium, and understanding the fluctuations in such systems is one of the fundamental problems of statistical physics that has challenged researchers for decades. Recent progress in the solution of this problem is closely related to the emerging understanding of patterns of deterministic trajectories underlying non-equilibrium fluctuations. These trajectories correspond to the Hamilton equations of motion written for the asymptotic solution of the Fokker - Planck equation and were often thought of as a mere mathematical abstraction. The possibility of quantitative experiments could not be entertained until the appropriate statistical quantity (prehistory probability distribution) had been introduced. In this paper it is shown how such trajectories can be measured experimentally in a number of systems and how the knowledge of these trajectories can be used to solve long standing problems in the theory of fluctuations and in the control theory.     

On a possible difference between the barycentric velocity and the velocity that gives translational momentum in fluids

This paper explores the rather controversial proposal by Howard Brenner that the velocities that follow from the mass flux and from the translational momentum in a fluid, are not equal. We show that standard non-equilibrium thermodynamics can be formulated such that it is in full agreement with this proposal. We argue that the merits of the proposal must be based on the physics of the problem. It cannot be dismissed as being in contradiction with non-equilibrium thermodynamics. We show that Brenners proposal gives a separation in a binary mixture beyond that of the Soret equilibrium, due to a gradient in the pressure divided by the temperature. Possible experiments to verify this are discussed.     

Stochastic equations in black hole backgrounds and non-equilibrium fluctuation theorems

We apply the non-equilibrium fluctuation theorems developed in the statistical physics to the thermodynamics of black hole horizons. In particular, we consider a scalar field in a black hole background. The system of the scalar field behaves stochastically due to the absorption of energy into the black hole and emission of the Hawking radiation from the black hole horizon. We derive the stochastic equations, i.e. Langevin and Fokker-Planck equations for a scalar field in a black hole background in the ?→0 limit with the Hawking temperature ?κ/2π fixed. We consider two cases, one confined in a box with a black hole at the center and the other in contact with a heat bath with temperature different from the Hawking temperature. In the first case, the system eventually becomes equilibrium with the Hawking temperature while in the second case there is an energy flow between the black hole and the heat bath. Applying the fluctuation theorems to these cases, we derive the generalized second law of black hole thermodynamics. In the present paper, we treat the black hole as a constant background geometry.Since the paper is also aimed to connect two different areas of physics, non-equilibrium physics and black holes physics, we include pedagogical reviews on the stochastic approaches to the non-equilibrium fluctuation theorems and some basics of black holes physics.     

Tops and Writhing DNA

The torsional elasticity of semiflexible polymers like DNA is of biological significance. A mathematical treatment of this problem was begun by Fuller using the relation between link, twist and writhe, but progress has been hindered by the non-local nature of the writhe. This stands in the way of an analytic statistical mechanical treatment, which takes into account thermal fluctuations, in computing the partition function. In this paper we use the well known analogy with the dynamics of tops to show that when subjected to stretch and twist, the polymer configurations which dominate the partition function admit a local writhe formulation in the spirit of Fuller and thus provide an underlying justification for the use of Fuller’s “local writhe expression” which leads to considerable mathematical simplification in solving theoretical models of DNA and elucidating their predictions. Our result facilitates comparison of the theoretical models with single molecule micromanipulation experiments and computer simulations.     

Dynamics of intramolecular recognition: Base-pairing in DNA/RNA near and far from equilibrium

The physics of the base-pairing interaction in DNA and RNA molecules plays a fundamental role in biology. Past experimental and theoretical research has led to a fairly complete and quantitative understanding of the equilibrium properties such as the different phases, the melting behavior, and the response to slow stretching. The non-equilibrium behavior is even richer than might be expected on the basis of thermodynamics. However, the non-equilibrium behavior is also far less understood. Here, we review different theoretical approaches to the study of base-pairing thermodynamics and kinetics, and illustrate the rich phenomenology with several examples that use these approaches.     

Statistical physics of human beings in games:Controlled experiments

It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings;making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system,thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.     

Emergence and collapse of quantum mechanical superposition: Orthogonality of reversible dynamics and irreversible diffusion

Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schrödinger dynamics and irreversible processes of diffusion. Moreover, the said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical “decay of the wave packet” is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle’s changing thermal environment. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet, as well as Born’s rule, are thus all derived solely from classical physics.     

非平衡凝固与固态相变中有关形核和长大的竞争研究

非平衡凝固和固态相变作为同热力学和动力学紧密相关的复杂理论体系,在物理冶金和凝聚态物理研究领域占据重要的地位。上述非平衡过程包含形核、生长和碰撞三个微观过程,其发生和发展均由一些竞争过程伴随、辅助甚至驱动。正确理解这些竞争过程决定了能否准确描述整个非平衡过程;材料制备中,其力学和物理/化学性能的提高也归根于这些竞争的发生与发展。因此,很有必要对非平衡凝固和固态相变中的竞争现象进行研究。本综述第一部分从形核/生长类相变角度对非平衡凝固和固态相变进行了概述,并强调了伴随其发生的竞争现象。第二部分立足于经典形核理论,对有关形核热力学、动力学以及形核方式的竞争现象进行了描述。第三部分对凝固中有关热扩散和溶质扩散以及固态相变中有关界面控制和扩散控制的生长方式竞争进行了描述。第四部分对本综述进行了总结性分析和概括,并对本领域的未来发展方向进行了预测。     

单分子操纵与单分子生物物理

文章介绍了近年来发展起来的一些单分子操纵实验技术如光镊、磁镊、微针、斯托克斯拖曳技术，以及应用这些技术拉伸、旋转、解链DNA分子，从而研究其力学性质所取得的研究进展．各种蛋白质如T7 DNA聚合酶、拓扑异构酶，SWI／SNF染色质重建复合体、RNA聚合酶与DNA的作用在生化过程中十分重要，因此，文章也介绍了这些蛋白质与DNA在单分子的水平上相互作用所取得的研究进展．     

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene

The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics. In this paper, by considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers. The results indicate that the first one can be interpreted as a measure of how fast the system is trying to approach the local equilibrium, while the second one as the local equilibrium lattice temperature. We also provide the explicit expression of the macroscopic entropy density for the system of phonons, by which we theoretically explain the approach of the system toward equilibrium and characterize the nature of the equilibria, in the spatially homogeneous case.     

Imaging and manipulation of biological structures with the AFM

Many biologists have dreamt of physically touching and manipulating the biomolecules they were investigating. With the invention of the atomic force microscope (AFM), this dream has come true. Here, recent applications of the AFM to image and to manipulate biological systems at the nanometer scale are reviewed. Macromolecular biological assemblies as well as individual biomolecules can be subjected to controlled nanomanipulation. Examples of AFM application in imaging and nanomanipulation include the extraction of chromosomal DNA for genetic analysis, the disruption of antibody--antigen bonds, the dissection of biological membranes, the nanodissection of protein complexes, and the controlled modulation of protein conformations. Also reviewed is the novel combination of single molecule imaging and force spectroscopy which allows biomolecules to be imaged, and inter- and intramolecular forces to be measured. Future application of these nanotechniques will reveal new information on the structure, function and assembly of biomolecules.     

一种改进型单分子操纵装置及其应用

改进了单分子横向磁镊装置,可以直接用于观察单个DNA分子的伸长和扭转并随时更换样品池内的溶液,还可以同时操纵多个DNA分子,大大提高实验效率.此方法可以提供01到40pN范围的拉力,足以满足大部分单分子DNA实验的要求.用该装置实时观测到了DNA分子在拉力作用下的伸长以及在旋转磁场作用下的扭转,并成功地观察到了分子马达拉动DNA的动力学过程,从而验证了该装置的实用性. 关键词： 横向磁镊 单分子操纵 DNA拉伸 DNA扭转     

Inverse statistical problems: from the inverse Ising problem to data science

Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.     

应用于单分子测序的纳米微结构器件

基因测序技术是现代最为重要的生物医学研究手段之一,单分子测序技术作为最新一代测序技术被广泛研究,并形成了微纳制造、光电子、微流控和分子生物学等多学科的交叉探索和多种技术创新的有机结合.文章系统总结了应用于单分子测序的纳米微结构器件的原理和功能,重点阐述了零模波导器件和纳米孔器件在单分子测序中的作用以及制备工艺,从器件的角度提出了单分子测序技术所面临的挑战.