Nonequilibrium temperature response for stochastic overdamped systems

The thermal response of nonequilibrium systems requires the knowledge of concepts that go beyond entropy production. This is showed for systems obeying overdamped Langevin dynamics, either in steady states or going through a relaxation process. Namely, we derive the linear response to perturbations of the noise intensity, mapping it onto the quadratic response to a constant small force. The latter, displaying divergent terms, is explicitly regularized with a novel path-integral method. The nonequilibrium equivalents of heat capacity and thermal expansion coefficient are two applications of this approach, as we show with numerical examples.Comment: 23 pages, 2 figure

On the Characteristic Isolation of Compact Subgroups within Loose Groups of Galaxies

We have explored the hypothesis that compact subgroups lying within dense environments as loose groups of galaxies, at a certain stage of their evolutionary history, could be influenced by the action of the tidal field induced by the gravitational potential of the whole system. We argue that empty rings observed in projection around many compact subgroups of galaxies embedded in larger hosts originate around the spherical surface drawn by the tidal radius where the internal binding force of the compact subgroup balances the external tidal force of the whole system. This effect would torn apart member galaxies situated in this region determining a marked isolation of the subgroups from the rest of the host groups. If so, subsequent evolution of these subgroups should not be affected by external influences as the infall of new surrounding galaxies on them. Following this idea we have developed a statistical method of investigation and performed an application to show evidences of such effect studying a loose group of galaxies hosting a compact group in its central region. The system UZC 578 / HCG 68 seems to be a fair example of such hypothesized process.Comment: 12 pages, match version accepted for publication in TOAJ, corrected typo

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.Comment: v3: published version, slightly shorter title and abstrac

A thermodynamic uncertainty relation for a system with memory

We introduce an example of thermodynamic uncertainty relation (TUR) for systems modeled by a one-dimensional generalised Langevin dynamics with memory, determining the motion of a micro-bead driven in a complex fluid. Contrary to TURs typically discussed in the previous years, our observables and the entropy production rate are one-time variables. The bound to the signal-to-noise ratio of such state-dependent observables only in some cases can be mapped to the entropy production rate. For example, this is true in Markovian systems. Hence, the presence of memory in the system complicates the thermodynamic interpretation of the uncertainty relation

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.Comment: 10 pages, 3 figure

A lattice polymer study of DNA renaturation dynamics

DNA renaturation is the recombination of two complementary single strands to form a double helix. It is experimentally known that renaturation proceeds through the formation of a double stranded nucleus of several base pairs (the rate limiting step) followed by a much faster zippering. We consider a lattice polymer model undergoing Rouse dynamics and focus on the nucleation of two diffusing strands. We study numerically the dependence of various nucleation rates on the strand lengths and on an additional local nucleation barrier. When the local barrier is sufficiently high, all renaturation rates considered scale with the length as predicted by Kramers' rate theory and are also in agreement with experiments: their scaling behavior is governed by exponents describing equilibrium properties of polymers. When the local barrier is lowered renaturation occurs in a regime of genuine non-equilibrium behavior and the scaling deviates from the rate theory prediction.Comment: 13 pages, 6 figures. To appear in Journal of Statistical Mechanic

Self-similar aftershock rates

In many important systems exhibiting crackling noise --- intermittent avalanche-like relaxation response with power-law and, thus, self-similar distributed event sizes --- the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is in particular true for the case of seismicity and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high resolution earthquake data from Southern California we find excellent agreement, providing in particular clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved way of time-dependent seismic hazard assessment and earthquake forecasting

Interplay between writhe and knotting for swollen and compact polymers

The role of the topology and its relation with the geometry of biopolymers under different physical conditions is a nontrivial and interesting problem. Aiming at understanding this issue for a related simpler system, we use Monte Carlo methods to investigate the interplay between writhe and knotting of ring polymers in good and poor solvents. The model that we consider is interacting self-avoiding polygons on the simple cubic lattice. For polygons with fixed knot type we find a writhe distribution whose average depends on the knot type but is insensitive to the length $N$ of the polygon and to solvent conditions. This "topological contribution" to the writhe distribution has a value that is consistent with that of ideal knots. The standard deviation of the writhe increases approximately as $\sqrt{N}$ in both regimes and this constitutes a geometrical contribution to the writhe. If the sum over all knot types is considered, the scaling of the standard deviation changes, for compact polygons, to $\sim N^{0.6}$. We argue that this difference between the two regimes can be ascribed to the topological contribution to the writhe that, for compact chains, overwhelms the geometrical one thanks to the presence of a large population of complex knots at relatively small values of $N$. For polygons with fixed writhe we find that the knot distribution depends on the chosen writhe, with the occurrence of achiral knots being considerably suppressed for large writhe. In general, the occurrence of a given knot thus depends on a nontrivial interplay between writhe, chain length, and solvent conditions.Comment: 10 pages, accepted in J.Chem.Phy

Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings

We introduce and implement a Monte Carlo scheme to study the equilibrium statistics of polymers in the globular phase. It is based on a model of "interacting elastic lattice polymers" and allows a sufficiently good sampling of long and compact configurations, an essential prerequisite to study the scaling behaviour of free energies. By simulating interacting self-avoiding rings at several temperatures in the collapsed phase, we estimate both the bulk and the surface free energy. Moreover from the corresponding estimate of the entropic exponent $\alpha-2$ we provide evidence that, unlike for swollen and $\Theta$-point rings, the hyperscaling relation is not satisfied for globular rings.Comment: 8 pages; v2: typos removed, published versio