arXiv subjects

Marco Baiesi

Publications and source records attributed to Marco Baiesi.

At least 55 records · Page 3Linked to original sources

arXiv2015

Inflow rate, a time-symmetric observable obeying fluctuation relations

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find detailed and integral fluctuation relations for the (time integrated) difference between "entrance rate" and escape rate in mesoscopic jump systems. Such "inflow rate", which is even under time reversal, represents the discrete-state equivalent of the phase space contraction rate. Indeed, it becomes minus the divergence of forces in the continuum limit to overdamped diffusion. This establishes a formal connection between reversible deterministic systems and irreversible stochastic ones, confirming that fluctuation theorems are largely independent of the details of the underling dynamics.

cond-mat.stat-mech↗

arXiv2015

Role of trapping and crowding as sources of negative differential mobility

Increasing the crowding in an environment does not necessarily trigger negative differential mobility of strongly pushed particles. Moreover, the choice of the model, in particular the kind of microscopic jump rates, may be very relevant in determining the mobility. We support these points via simple examples and we therefore address recent claims saying that crowding in an environment is likely to promote negative differential mobility. Trapping of tagged particles enhanced by increasing the force remains the mechanism determining a drift velocity not monotonous in the driving force.

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arXiv2015

Temperature response in nonequilibrium stochastic systems

The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from unperturbed correlation functions. These correlations contain a novel form of entropy flow due to temperature unbalances, next to the standard entropy flow of stochastic energetics and to complementary time-symmetric dynamical aspects. Our derivation hinges on a time rescaling, which is a key procedure for comparing apparently incommensurable path weights. An interesting notion of thermal time emerges from this approach.

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arXiv2015

Energy repartition for a harmonic chain with local reservoirs

We exactly analyze the vibrational properties of a chain of harmonic oscillators in contact with local Langevin heat baths. Nonequilibrium steady-state fluctuations are found to be described by a set of mode-temperatures, independent of the strengths of both the harmonic interaction and the viscous damping. Energy is equally distributed between the conjugate variables of a given mode but differently among different modes, in a manner which depends exclusively on the bath temperatures and on the boundary conditions. We outline how bath-temperature profiles can be designed to enhance or reduce fluctuations at specific frequencies in the power spectrum of the chain length.

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arXiv2014

Rings in Random Environments: Sensing Disorder Through Topology

In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby generating a disordered environment. Changes in the microscopic structure of the gel are captured by measuring the electrophoretic mobility of ring polymers moving through the medium, while their linear counterparts provide a control system as we show they are insensitive to these changes. We show that ring polymers provide a novel non-invasive way of exploiting topology to sense microscopic disorder. Finally, we compare the results from the simulations with an analytical model for the non-equilibrium differential mobility, and find a striking agreement between simulation and theory

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arXiv2014

Knotted globular ring polymers: how topology affects statistics and thermodynamics

The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature $T$, in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low $T$ on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops (preserving their topology) which compete for the chain length, either in contact or separated by a wall as for translocation through a membrane pore. These findings suggest that in macromolecular environments there may be entropic forces with a purely topological origin, whence portions of polymers holding complex knots should tend to expand at the expense of significantly shrinking other topologically simpler portions.

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arXiv2014

Thermal response in driven diffusive systems

Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast relaxing mechanical, chemical or thermal equilibrium reservoirs. Modifying one of the temperatures creates both entropy fluxes and changes in dynamical activity. That is not unlike mechanical response of nonequilibrium systems but the extra difficulty for perturbation theory via path-integration is that for a Langevin dynamics temperature also affects the noise amplitude and not only the drift part. Using a discrete-time mesh adapted to the numerical integration one avoids that ultraviolet problem and we arrive at a fluctuation expression for its thermal susceptibility. The algorithm appears stable under taking even finer resolution.

cond-mat.stat-mech↗

arXiv2014

Rotational dynamics of entangled polymers

Some recent results on the rotational dynamics of polymers are reviewed and extended. We focus here on the relaxation of a polymer, either flexible or semiflexible, initially wrapped around a rigid rod. We also study the steady polymer rotation generated by a constant torque on the rod. The interplay of frictional and entropic forces leads to a complex dynamical behavior characterized by non-trivial universal exponents. The results are based on extensive simulations of polymers undergoing Rouse dynamics and on an analytical approach using force balance and scaling arguments. The analytical results are in general in good agreement with the simulations, showing how a simplified approach can correctly capture the complex dynamical behavior of rotating polymers.

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arXiv2014

Unwinding Dynamics of a Helically Wrapped Polymer

We study the rotational dynamics of a flexible polymer initially wrapped around a rigid rod and unwinding from it. This dynamics is of interest in several problems in biology and constitutes a fundamental instance of polymer relaxation from a state of minimal entropy. We investigate the dynamics of several quantities such as the total and local winding angles and metric quantities. The results of simulations performed in two and three dimensions, with and without self-avoidance, are explained by a theory based on scaling arguments and on a balance between frictional and entropic forces. The early stage of the dynamics is particularly rich, being characterized by three coexisting phases.

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arXiv2014

Models of DNA denaturation dynamics: universal properties

We briefly review some of the models used to describe DNA denaturation dynamics, focusing on the value of the dynamical exponent $z$, which governs the scaling of the characteristic time $τ\sim L^z$ as a function of the sequence length $L$. The models contain different degrees of simplifications, in particular sometimes they do not include a description for helical entanglement: we discuss how this aspect influences the value of $z$, which ranges from $z=0$ to $z \approx 3.3$. Connections with experiments are also mentioned.

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arXiv2013

Unwinding relaxation dynamics of polymers

The relaxation dynamics of a polymer wound around a fixed obstacle constitutes a fundamental instance of polymer with twist and torque and it is of relevance also for DNA denaturation dynamics. We investigate it by simulations and Langevin equation analysis. The latter predicts a relaxation time scaling as a power of the polymer length times a logarithmic correction related to the equilibrium fluctuations of the winding angle. The numerical data support this result and show that at short times the winding angle decreases as a power-law. This is also in agreement with the Langevin equation provided a winding-dependent friction is used, suggesting that such reduced description of the system captures the basic features of the problem.

cond-mat.soft↗

arXiv2012

Universal properties of knotted polymer rings

By performing Monte Carlo sampling of $N$-steps self-avoiding polygons embedded on different Bravais lattices we explore the robustness of universality in the entropic, metric and geometrical properties of knotted polymer rings. In particular, by simulating polygons with $N$ up to $10^5$ we furnish a sharp estimate of the asymptotic values of the knot probability ratios and show their independence on the lattice type. This universal feature was previously suggested although with different estimates of the asymptotic values. In addition we show that the scaling behavior of the mean squared radius of gyration of polygons depends on their knot type only through its correction to scaling. Finally, as a measure of the geometrical self-entanglement of the SAPs we consider the standard deviation of the writhe distribution and estimate its power-law behavior in the large $N$ limit. The estimates of the power exponent do depend neither on the lattice nor on the knot type, strongly supporting an extension of the universality property to some features of the geometrical entanglement.

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arXiv2012

An update on nonequilibrium linear response

The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second "probabilistic" approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to linear response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition.

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arXiv2012

Fibril elongation mechanisms of HET-s prion-forming domain: Topological evidence for growth polarity

The prion-forming C-terminal domain of the fungal prion HET-s forms infectious amyloid fibrils at physiological pH. The conformational switch from the non-prion soluble form to the prion fibrillar form is believed to have a functional role, since HET-s in its prion form participates in a recognition process of different fungal strains. Based on the knowledge of the high-resolution structure of HET-s(218-289) (the prion forming-domain) in its fibrillar form, we here present a numerical simulation of the fibril growth process which emphasizes the role of the topological properties of the fibrillar structure. An accurate thermodynamic analysis of the way an intervening HET-s chain is recruited to the tip of the growing fibril suggests that elongation proceeds through a dock and lock mechanism. First, the chain docks onto the fibril by forming the longest $β$-strands. Then, the re-arrangement in the fibrillar form of all the rest of molecule takes place. Interestingly, we predict also that one side of the HET-s fibril is more suitable for substaining its growth with respect to the other. The resulting strong polarity of fibril growth is a consequence of the complex topology of HET-s fibrillar structure, since the central loop of the intervening chain plays a crucially different role in favouring or not the attachment of the C-terminus tail to the fibril, depending on the growth side.

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arXiv2011

The modified Sutherland--Einstein relation for diffusive nonequilibria

There remains a useful relation between diffusion and mobility for a Langevin particle in a periodic medium subject to nonconservative forces. The usual fluctuation-dissipation relation easily gets modified and the mobility matrix is no longer proportional to the diffusion matrix, with a correction term depending explicitly on the (nonequilibrium) forces. We discuss this correction by considering various simple examples and we visualize the various dependencies on the applied forcing and on the time by means of simulations. For example, in all cases the diffusion depends on the external forcing more strongly than does the mobility. We also give an explicit decomposition of the symmetrized mobility matrix as the difference between two positive matrices, one involving the diffusion matrix, the other force--force correlations.

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arXiv2010

Elastic Lattice Polymers

We study a model of "elastic" lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density $ρ_m = 1 - /m$ scales asymptotically for large $m$ as $ρ_m=ρ_\infty(1-θ/m + ...)$, where $θ$ is the polymer entropic exponent, so that $θ$ can be determined from the analysis of $ρ_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $ρ_m$. The resulting estimates support the hypothesis that the exponent $θ$ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain.

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arXiv2010

The entropic cost to tie a knot

We estimate by Monte Carlo simulations the configurational entropy of $N$-steps polygons in the cubic lattice with fixed knot type. By collecting a rich statistics of configurations with very large values of $N$ we are able to analyse the asymptotic behaviour of the partition function of the problem for different knot types. Our results confirm that, in the large $N$ limit, each prime knot is localized in a small region of the polygon, regardless of the possible presence of other knots. Each prime knot component may slide along the unknotted region contributing to the overall configurational entropy with a term proportional to $\ln N$. Furthermore, we discover that the mere existence of a knot requires a well defined entropic cost that scales exponentially with its minimal length. In the case of polygons with composite knots it turns out that the partition function can be simply factorized in terms that depend only on prime components with an additional combinatorial factor that takes into account the statistical property that by interchanging two identical prime knot components in the polygon the corresponding set of overall configuration remains unaltered. Finally, the above results allow to conjecture a sequence of inequalities for the connective constants of polygons whose topology varies within a given family of composite knot types.

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arXiv2009

Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions

Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. The resulting response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics, but in this first part they are restricted to Markov jump processes and overdamped diffusions.

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