Equilibrium Thermal Fluctuations Research Articles

Controlling dispersion forces between small particles with artificially created random light fields.

Appropriate combinations of laser beams can be used to trap and manipulate small particles with optical tweezers as well as to induce significant optical binding forces between particles. These interaction forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic, translationally invariant, van der Waals and, in general, Casimir–Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. Here we show, both theoretically and experimentally, that dispersion forces between small colloidal particles can also be induced and controlled using artificially created fluctuating light fields. Using optical tweezers as a gauge, we present experimental evidence for the predicted isotropic attractive interactions between dielectric microspheres induced by laser-generated, random light fields. These light-induced interactions open a path towards the control of translationally invariant interactions with tuneable strength and range in colloidal systems.

Thermal dispersion potential of a diamagnetic atom

We study the diamagnetic interaction between a ground-state atom, which is located at a distance $z$ from a planar body, e.g., a perfect mirror or a nondispersive and nonabsorbing dielectric substrate, and the body-assisted electromagnetic fields from vacuum, equilibrium, and out of equilibrium thermal fluctuations. We find that the diamagnetic potential at zero temperature is always proportional to ${z}^{\ensuremath{-}4}$ in both the retarded and the nonretarded zones, and the Casimir-Polder (CP) force is attractive. The CP potential due to the thermal fluctuations at equilibrium dominates over that due to the zero-point fluctuations in the long-distance or high-temperature limit and behaves like $T/{z}^{3}$, and the corresponding force is attractive. However, in the case of out of thermal equilibrium, the CP potential exhibits a different behavior with slower dependence on the distance and stronger dependence on temperature in the same limit, and it decays like $({T}_{e}^{2}\ensuremath{-}{T}_{s}^{2})/{z}^{2}$, where ${T}_{e}$ is the temperature of the environment and ${T}_{s}$ is that of the substrate, yielding a CP force that can either be attractive or repulsive. Meanwhile, in the short-distance or low-temperature limit the CP potential is always dominated by the contribution due to the vacuum fluctuations.

Rheology of semiflexible bundle networks with transient linkers.

We present a theoretical and computational analysis of the rheology of networks made up of bundles of semiflexible filaments bound by transient cross-linkers. Such systems are ubiquitous in the cytoskeleton and can be formed in vitro using filamentous actin and various cross-linkers. We find that their high-frequency rheology is characterized by a scaling behavior that is quite distinct from that of networks of the well-studied single semiflexible filaments. This regime can be understood theoretically in terms of a length-scale-dependent bending modulus for bundles. Next, we observe new dissipative dynamics associated with the shear-induced disruption of the network at intermediate frequencies. Finally, at low frequencies, we encounter a region of non-Newtonian rheology characterized by power-law scaling. This regime is dominated by bundle dissolution and large-scale rearrangements of the network driven by equilibrium thermal fluctuations.

Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to have strong correlations between equilibrium thermal fluctuations of virial and potential energy. Such systems have good isomorphs (curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units). The SLLOD equations of motion were used to simulate Couette shear flows of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of strain rates were simulated to test for the predicted invariance, covering both the linear and nonlinear regimes. For both systems, when represented in reduced units the radial distribution function and the intermediate scattering function are identical for state points that are isomorphic. The strain-rate dependent viscosity, which exhibits shear thinning, is also invariant along an isomorph. Our results extend the isomorph concept to the non-equilibrium situation of a shear flow, for which the phase diagram is three dimensional because the strain rate defines a third dimension.

Fluctuation current in superconducting loops

A superconducting loop that encloses noninteger flux holds a permanent current. On the average, this current is also present above Tc, and has been measured in recent years. We are able to evaluate the permanent current within the TDGL or the Kramer-Watts-Tobin models for loops of general configuration, i.e., we don't require uniform cross section, material or temperature. We can also consider situations in which the width is not negligible in comparison to the radius. Our results agree with experiments. The situations with which we deal at present include fluctuation superconductivity in two-band superconductors, equilibrium thermal fluctuations of supercurrent along a weak link, and ratchet effects.

Statistics of the population difference for cold fermions in a double well potential

Sensitive measurements of the density fluctuations in ultracold gases performed recently evidenced quantum statistical effects, i.e. an enhancement of the density fluctuations in Bose gas and a suppression of the fluctuations in Fermi gas. In this paper we study thermal equilibrium fluctuations in the atomic number difference between the two halves of a harmonically trapped Fermi gas split by a delta potential. We show how splitting the potential strength affects the fluctuations.

Relaxation in finite and isolated classical systems: An extension of Onsager's regression hypothesis

In order to derive the reciprocity relations, Onsager formulated a relation between thermal equilibrium fluctuations and relaxation widely known as regression hypothesis. It is shown in the present work how such a relation can be extended to finite and isolated classical systems. This extension is derived from the fluctuation-dissipation theorem for the microcanonical ensemble. The results are exemplified with a nonintegrable system in order to motivate possible applications to dynamical systems and statistical mechanics of finite systems.

Entropic Corrections to Coulomb’s Law

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde's argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb's law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb's law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb's law as well as the entropy corrected Poisson's equation which governing the evolution of the scalar potential $\phi$. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.

Determination of Viral Capsid Elastic Properties from Equilibrium Thermal Fluctuations

We apply two-dimensional elasticity theory to viral capsids to develop a framework for calculating elastic properties of viruses from equilibrium thermal fluctuations of the capsid surface in molecular dynamics and elastic network model trajectories. We show that the magnitudes of the long wavelength modes of motion available in a simulation with all atomic degrees of freedom are recapitulated by an elastic network model. For the mode spectra to match, the elastic network model must be scaled appropriately by a factor which can be determined from an icosahedrally constrained all-atom simulation. With this method we calculate the two-dimensional Young's modulus Y, bending modulus κ, and Föppl-von Kármán number γ, for the T=1 mutant of the Sesbania mosaic virus. The values determined are in the range of previous theoretical estimates.

Conformational Dynamics and Allostery of Supramolecular Protein Assemblies: from the Nuclear Pore Complex to GroEL

Supramolecular protein assemblies participate in a broad range of cellular functions including transcription, translation, protein synthesis and folding, translocation of biomolecules, and cell division. Single particle cryo-electron microscopy is increasingly revealing the structure of diverse high molecular weight protein assemblies at ever higher resolution. While the static structure of these assemblies provides invaluable insight into their functional mechanism, important additional information is provided by their conformational dynamics. Here we present an unsupervised computational framework that is used to analyze the conformational dynamics of the majority of structures deposited in the Electron Microscopy Data Bank. Conformational dynamics are computed using normal mode analysis based on a recently established finite element framework, which is used to compute equilibrium thermal fluctuations, elastic strain energy distributions associated with specific conformational transitions, and dynamical correlations in distant molecular domains. Results are presented in detail for the nuclear pore complex from Dictyostelium discoideum and the chaperonin GroEL from Escherichia coli, revealing regions that are important to the stability of these molecules, as well as highly coupled dynamically in collective molecular motions. Results are publically available at http://www.cdyn.org and will be extended to include proteins in the Protein Data Bank, offering an important source of dynamical information that may be used to investigate the biological function of a broad range of molecules.

Stretching and relaxation of vesicles

We study the shape relaxation of spherical giant unilamellar vesicles which have been deformed far from equilibrium into ellipsoids using optical tweezers. The relaxation back to a sphere is determined by elastic constants of the vesicles, and their excess area, parameters that are obtained for each stretched vesicle from shape fluctuations in thermal equilibrium, as well as low Reynolds number fluid flow. The relaxation time could be compared favorably to a simple formula which encompasses the joint effect of membrane rigidity and fluid flow. The time constant of the stretched vesicle is slower than that of its thermal fluctuations, which agrees with a recent theory; however, it is one order of magnitude faster than predicted.

Conformational dynamics data bank: a database for conformational dynamics of proteins and supramolecular protein assemblies.

The conformational dynamics data bank (CDDB, http://www.cdyn.org) is a database that aims to provide comprehensive results on the conformational dynamics of high molecular weight proteins and protein assemblies. Analysis is performed using a recently introduced coarse-grained computational approach that is applied to the majority of structures present in the electron microscopy data bank (EMDB). Results include equilibrium thermal fluctuations and elastic strain energy distributions that identify rigid versus flexible protein domains generally, as well as those associated with specific functional transitions, and correlations in molecular motions that identify molecular regions that are highly coupled dynamically, with implications for allosteric mechanisms. A practical web-based search interface enables users to easily collect conformational dynamics data in various formats. The data bank is maintained and updated automatically to include conformational dynamics results for new structural entries as they become available in the EMDB. The CDDB complements static structural information to facilitate the investigation and interpretation of the biological function of proteins and protein assemblies essential to cell function.

Conformational dynamics of supramolecular protein assemblies

Supramolecular protein assemblies including molecular motors, cytoskeletal filaments, chaperones, and ribosomes play a central role in a broad array of cellular functions ranging from cell division and motility to RNA and protein synthesis and folding. Single-particle reconstructions of such assemblies have been growing rapidly in recent years, providing increasingly high resolution structural information under native conditions. While the static structure of these assemblies provides essential insight into their mechanism of biological function, their dynamical motions provide additional important information that cannot be inferred from structure alone. Here we present an unsupervised computational framework for the analysis of high molecular weight protein assemblies and use it to analyze the conformational dynamics of structures deposited in the Electron Microscopy Data Bank. Protein assemblies are modeled using a recently introduced coarse-grained modeling framework based on the finite element method, which is used to compute equilibrium thermal fluctuations, elastic strain energy distributions associated with specific conformational transitions, and dynamical correlations in distant molecular domains. Results are presented in detail for the ribosome-bound termination factor RF2 from Escherichia coli, the nuclear pore complex from Dictyostelium discoideum, and the chaperonin GroEL from E. coli. Elastic strain energy distributions reveal hinge-regions associated with specific conformational change pathways, and correlations in collective molecular motions reveal dynamical coupling between distant molecular domains that suggest new, as well as confirm existing, allosteric mechanisms. Results are publically available for use in further investigation and interpretation of biological function including cooperative transitions, allosteric communication, and molecular mechanics, as well as in further classification and refinement of electron microscopy based structures.

Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams

This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the phase diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and co-workers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, and it explains isochronal superposition for strongly correlating viscous liquids.

Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance

In this third paper of the series, which started with Bailey et al. [J. Chem. Phys. 129, 184507 (2008); ibid. 129, 184508 (2008)], we continue the development of the theoretical understanding of strongly correlating liquids--those whose instantaneous potential energy and virial are more than 90% correlated in their thermal equilibrium fluctuations at constant volume. The existence of such liquids was detailed in previous work, which identified them, based on computer simulations, as a large class of liquids, including van der Waals liquids but not, e.g., hydrogen-bonded liquids. We here discuss the following: (1) the scaling properties of inverse power-law and extended inverse power-law potentials (the latter includes a linear term that "hides" the approximate scale invariance); (2) results from computer simulations of molecular models concerning out-of-equilibrium conditions; (3) ensemble dependence of the virial/potential-energy correlation coefficient; (4) connection to the Grüneisen parameter; and (5) interpretation of strong correlations in terms of the energy-bond formalism.

Allosteric Coupling and Conformational Fluctuations in Proteins

Proteins in their native folded states can possess multiple energy minima and they can show constant conformational fluctuations at physiological temperatures. In this article, we discuss the quantitative relationship between ligand-induced perturbation of such fluctuations, modeled as probability distributions of conformational substates, and allosteric coupling of ligand binding to different sites, as defined by linkage thermodynamics. We show that allosteric coupling between two binding events on the same protein is an inevitable consequence of ligand-induced perturbations of the probability distribution that represents conformational fluctuations in thermal equilibrium. When high resolution structural data of a protein in empty and ligand-bound forms are available, the COREX algorithm can provide, in principle, an excellent bridge between the energetics of substates distribution in the protein ensemble and structural coordinates. Here we propose a COREX-based strategic approach to link structural perturbations and the free energy changes of allosteric coupling. This strategy might be broadly useful in the endeavor of predicting how specific ligands allosterically regulate the function of specific proteins.

An in vitro model system for cytoskeletal confinement

The motility, shape, and functionality of the cell depend sensitively on cytoskeletal mechanics which in turn is governed by the properties of filamentous proteins - mainly actin, microtubules, and intermediate filaments. These biopolymers are confined in the dense cytoplasm and therefore experience strong geometric constraints on their equilibrium thermal fluctuations. To obtain a better understanding of the influence of confinement on cytoskeletal filaments we study the thermal fluctuations of individual actin filaments in a microfluidic in vitro system by fluorescence microscopy and determine the persistence length of the filaments by analyzing the radial distribution function. A unique feature of this method is that we obtain the persistence length without detailed knowledge of the complete contour of the filament which makes the technique applicable to a broad range of biological polymers, including those with a persistence length smaller than the optical resolution.

Coherent optical control of correlation waves of spins in semiconductors

We calculate the dynamical fluctuation spectrum of electronic spins in a semiconductor under a steady-state illumination by light containing polarization squeezing correlations. Taking into account quasiparticle lifetime and spin relaxation for this nonequilibrium situation we consider up to fourth order optical effects which are sensitive to the squeezing phases. We demonstrate the possibility to control the spin fluctuations by optically modulating these phases as a function of frequency, leading to a non-Lorentzian spectrum which is very different from the thermal equilibrium fluctuations in $n$-doped semiconductors. Specifically, in the time-domain spin-spin correlation can exhibit time delays and sign flips originating from the phase modulations and correlations of polarizations, respectively. For higher light intensity we expect a regime where the squeezing correlations will dominate the spectrum.

Glass-forming liquids: one or more ‘order’ parameters?

We first summarize the classical arguments that the vast majority of glass-forming liquidsrequire more than one ‘order’ parameter for their description. Critiques against thisconventional wisdom are then presented, and it is argued that the matter deserves to bereconsidered in the light of recent experimental developments. Out of the eight basicthermoviscoelastic frequency-dependent response functions, there are generally threeindependent functions. For stochastic dynamics we show that there are only twoindependent response functions; for this case it is shown how analytic continuation may beutilized to express the third response functions in terms of two others. Operationalcriteria are presented for the linear thermoviscoelasticity being described by a single‘order’ parameter, in which case there is just one independent thermoviscoelasticresponse function. It is shown that a description with a single ‘order’ parameterapplies to a good approximation whenever thermal equilibrium fluctuations offundamental variables like energy and pressure are strongly correlated. Resultsfrom computer simulations showing that this is the case for a number of simpleglass-forming liquids, as well as a few exceptions, are briefly presented. Finally,we briefly discuss a new conjecture according to which experiments at varyingtemperature and pressure follow the density scaling expression for the relaxation time,τ = F(ρx/T) (ρ and T are density and temperature), if and only if the liquid is ‘strongly correlating’, i.e., to agood approximation is described by a single ‘order’ parameter.

Micro- and nanoinhomogenities in glasses and their melts studied by optical, SAXS, acoustical and thermodynamic methods

Ultrasonic waves velocities are studied in glasses of the systems Na2O - GeO2 and K2O - GeO2 and in glasses and melts of the system PbO-GeO2. Our Rayleigh-Mandelshtam-Brillouin light scattering (RMBS), small angle X-ray scattering (SAXS) and Raman scattering (RS) experimental data for glasses of the system PbO-GeO2 have been analyzed. At small concentrations of metallic oxides a ‘‘water-like anomaly’’ is observed, i.e. the increase of sound velocity with raising temperature. The results of scattering are compared with calculations based on the concept of ‘‘frozen-in’’ equilibrium thermal fluctuations as the origin of static inhomogeneities in glasses. Discussion of glass composition dependences of the data obtained was performed in terms of ‘‘freezing’’ equilibrium thermodynamic fluctuations of density and concentration (chemical composition) in a glass melt at the process of its cooling and transformation into solid state. Usage of acoustic and electrochemical data for glass melts makes it possible to estimate contributions of ‘‘frozen-in’’ density and concentration fluctuations into Rayleigh scattering losses separately. Combining RMBS and RS data gave the answer to the important question: concentration of which structural species fluctuates in a glass melt? It was found that RS spectra of glasses contain information about units of a glass - groups with constant stoichiometry. These groups are characterized by components of the RS spectra intensities of which correspond with concentration of these groups. It means that some multicomponent glasses built from the groups of a single type. As a rule, these glasses are characterized by high level of chemical (and optical) homogeneity