Fluctuation-dissipation relation and stationary distribution for an exactly solvable many-particle model far from equilibrium

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution as well as the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution, which is possible because the model derives from a particle Hamiltonian. The difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e. deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter \alpha that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates, the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energyconsuming protein motors. The comparison is excellent and allows to extract the non-equilibrium parameter \alpha from experimental spectral response and fluctuation data

Polyelectrolytes Adsorption: Chemical and Electrostatic Interactions

Mean-field theory is used to model polyelectrolyte adsorption and the possibility of overcompensation of charged surfaces. For charged surfaces that are also chemically attractive, the overcharging is large in high salt conditions, amounting to 20-40% of the bare surface charge. However, full charge inversion is not obtained in thermodynamical equilibrium for physical values of the parameters. The overcharging increases with addition of salt, but does not have a simple scaling form with the bare surface charge. Our results indicate that more evolved explanation is needed in order to understand polyelectrolyte multilayer built-up. For strong polymer-repulsive surfaces, we derive simple scaling laws for the polyelectrolyte adsorption and overcharging. We show that the overcharging scales linearly with the bare surface charge, but its magnitude is very small in comparison to the surface charge. In contrast with the attractive surface, here the overcharging is found to decrease substantially with addition of salt. In the intermediate range of weak repulsive surfaces, the behavior with addition of salt crosses over from increasing overcharging (at low ionic strength) to decreasing one (at high ionic strength). Our results for all types of surfaces are supported by full numerical solutions of the mean-field equations.Comment: 17 pages, 7 figures, final version. to be published in PR

Multiple surface wave solutions on linear viscoelastic media

We study the generic dispersion relation of surface waves on a semi-infinite viscoelastic medium bounded by a 2D viscoelastic interface, including the effects of gravitation, surface tension and bending rigidity. The classical Rayleigh, capillary-gravity and Lucassen wave solutions result as limiting cases. We identify an additional solution that differs from all previously described waves in that gravitation, surface tension and bulk shear viscosity must simultaneously be nonzero, and which exists on a pure air-water interface. For a surfactant monolayer on water, the number of coexisting wave solutions switches between one and three, depending on interfacial compressibility and frequency

Unfolding and Folding Internal Friction of β‑Hairpins Is Smaller than That of α‑Helices

By the forced unfolding of polyglutamine and polyalanine homopeptides in competing α-helix and β-hairpin secondary structures, we disentangle equilibrium free energetics from nonequilibrium dissipative effects. We find that α-helices are characterized by larger friction or dissipation upon unfolding, regardless of whether they are free energetically preferred over β-hairpins or not. Our analysis, based on MD simulations for atomistic peptide models with explicit water, suggests that this difference is related to the internal friction and mostly caused by the different number of intrapeptide hydrogen bonds in the α-helix and β-hairpin states

Cyclization dynamics of finite-length collapsed self-avoiding polymers

We study the end-point cyclization of ideal and interacting polymers as a function of chain length N. For the cyclization time �cyc of ideal chains we recover the known scaling �cyc � N2 for different backbone models, for a self-avoiding slightly collapsed chain we obtain from Langevin simulations and scaling theory a modified scaling �cyc � N5=3. By extracting the memory kernel that governs the non-Markovian end-point kinetics, we demonstrate that the dynamics of a finite-length collapsed chain is dominated by the crossover between swollen and collapsed behavior

Nonlinear fractional waves at elastic interfaces

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface

Butane dihedral angle dynamics in water is dominated by internal friction

The dihedral dynamics of butane in water is known to be rather insensitive to the water viscosity, possible explanations for this involve inertial effects or Kramers’ turnover, the finite memory time of friction, and the presence of so-called internal friction. In order to disentangle these factors, we introduce a method to directly extract the friction memory function from simulations in the presence of an arbitrary free-energy landscape. By analysis of the dihedral friction in butane for varying water viscosity, we demonstrate the existence of an internal friction contribution. At normal water viscosity the internal friction turns out to be eight times larger than the solvent friction and thus completely dominates the effective friction. By comparison with simulations of a constrained butane molecule that has the dihedral as the only degree of freedom, we show that internal friction comes from the six additional degrees of freedom in unconstrained butane that are orthogonal to the dihedral angle reaction coordinate. While the insensitivity of butane’s dihedral dynamics to water viscosity is solely due to the presence of internal friction, inertial effects nevertheless crucially influence the resultant transition rates. In contrast, non-Markovian effects due to the finite memory time are present but do not significantly influence the dihedral barrier crossing rate of butane. These results not only settle the character of dihedral dynamics in small molecular systems such as butane, they also have important implications for the folding of polymers and protein

Markov state modeling reveals competing collective hydrogen bond rearrangements in liquid water

We construct a Markov state model for the dynamic rearrangement of the local hydrogen bond network in liquid water. The model is based on trajectories from classical molecular dynamics simulations and accounts for the dynamics of relative angular and separation coordinates of water molecules. We analyze first the conformational subspace of three water molecules and find five well separated dynamic modes with reaction times in the 2 - 5 ps range, which correspond to different interchanges of hydrogen bond donor and acceptors, followed by an entire continuum spectrum of modes. We then analyze the switching of one hydrogen bond between two water molecules and derive the complete transition network. The most probable pathway corresponds to a direct switch without an intermediate, in agreement with previous studies. However, a considerable fraction of paths proceeds along different intermediate states that involve alternative hydrogen bonds or unbound states

Surface states in nearly modulated systems

A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a non-wet layer having a small deviation from bulk order, and a different non-wet layer with a large deviation from bulk order which decays non-monotonically as distance from the wall increases. In particular the large deviation non-wet layer is a feature of systems at the Lifshitz point and also those having only homogeneous bulk phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.