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The overdamped Brownian dynamics of a harmonic oscillator is a paradigmatic system in non-equilibrium statistical mechanics, which reliably models relevant stochastic systems such as colloidal particles submitted to optical confinement. In this work, optimal thermal protocols are tailored to minimise the connection time between equilibrium states of overdamped d-dimensional oscillators. Application of control theory reveals that these optimal protocols are of bang-bang type, that is, the temperature of the bath has to take alternatively the minimum and maximum values allowed. Minimum connection times increase with the considered dimension d. Remarkably, this is the case even for symmetric oscillators, for example, with spherical symmetry—in which the degeneracy of the elastic constant along the d possible directions seems to imply a minimum connection time equal to that for the one-dimensional case. This surprising unavoidable price to pay when increasing dimension is thoroughly investigated and understood on a physical basis. Moreover, information theory tools such as the thermodynamic length and its divergence are analysed over the brachistochrone.

Scanning tunneling microscopy experiments have revealed an spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyse an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimisation of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analysed, both analytically and numerically. All phases are characterised by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene., Comment: 18 pages, 8 figures

Loosely speaking, the Mpemba effect appears when hotter systems cool sooner or, in a more abstract way, when systems further from equilibrium relax faster. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically (by employing the tools of kinetic theory) and numerically (direct simulation Monte Carlo of the kinetic equation and event-driven molecular dynamics). The analysis is carried out via two alternative routes, recently considered in the literature: first, the kinetic or thermal route, in which the Mpemba effect is characterized by the crossing of the evolution curves of the kinetic temperature (average kinetic energy), and, second, the stochastic thermodynamics or entropic route, in which the Mpemba effect is characterized by the crossing of the distance to equilibrium in probability space. In general, a nonmutual correspondence between the thermal and entropic Mpemba effects is found, i.e., there may appear the thermal effect without its entropic counterpart or vice versa. Furthermore, a nontrivial overshoot with respect to equilibrium of the thermal relaxation makes it necessary to revise the usual definition of the thermal Mpemba effect, which is shown to be better described in terms of the relaxation of the local equilibrium distribution. Our theoretical framework, which involves an extended Sonine approximation in which not only the excess kurtosis but also the sixth cumulant is retained, gives an excellent account of the behavior observed in simulations., Comment: 26 pages (including five appendices with 7 pages); 20 figures; v2: two new figures added, one new appendix, changes in the main text and in some figures

Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution towards a well chosen common intermediate state, we derive analytically a smooth protocol to connect two \emph{arbitrary} states in an arbitrarily short amount of time. Not only does the reverse-engineering approach proposed in this Letter contain the current -- rather limited -- catalogue of explicit protocols but it also provides a systematic strategy to build the connection between arbitrary states with a physically admissible driving. Optimization and further generalizations are also discussed., 6 pages+supplemental material; accepted for publication in Physical Review Letters

We analyse the dynamical evolution of a fluid with non-linear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of non-linear Brownian motion, displays a really complex behaviour when quenched to low temperatures. Its glassy response is controlled by a long-lived non-equilibrium state, independent of the degree of non-linearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behaviour persists in the collisionless case, where the fluid is described by the non-linear Fokker-Planck equation. The observed response, which includes non-exponential, algebraic, relaxation and strong memory effects, presents scaling properties: the time evolution of the temperature -- for both relaxation and memory effects -- falls onto a master curve, regardless of the details of the experiment. To account for the observed behaviour in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation -- which considers not only the fourth cumulant but also the sixth one., Comment: 18 pages, 14 figures; accepted as regular article in PRE

International audience; We analyse non-equilibrium Carnot-like cycles built with a colloidal particle in a harmonic trap, which is immersed in a fluid that acts as a heat bath. Our analysis is carried out in the overdamped regime. The cycle comprises four branches: two isothermal processes and two \textit{locally} adiabatic ones. In the latter, both the temperature of the bath and the stiffness of the harmonic trap vary in time, but in such a way that the average heat vanishes for all times. All branches are swept at a finite rate and, therefore, the corresponding processes are irreversible, not quasi-static. Specifically, we are interested in optimising the heat engine to deliver the maximum power and characterising the corresponding values of the physical parameters. The efficiency at maximum power is shown to be very close to the Curzon-Ahlborn bound over the whole range of the ratio of temperatures of the two thermal baths, pointing to the near optimality of the proposed protocol.

We look into the Mpemba effect---the initially hotter sample cools sooner---in a molecular gas with nonlinear viscous drag. Specifically, the gas particles interact among them via elastic collisions and also with a background fluid at equilibrium. Thus, within the framework of kinetic theory, our gas is described by an Enskog--Fokker--Planck equation. The analysis is carried out in the first Sonine approximation, in which the evolution of the temperature is coupled to that of the excess kurtosis. This coupling leads to the emergence of the Mpemba effect, which is observed in an early stage of the relaxation and when the initial temperatures of the two samples are close enough. This allows for the development of a simple theory, linearizing the temperature evolution around a reference temperature---namely the initial temperature closer to the asymptotic equilibrium value. The linear theory provides a semiquantitative description of the effect, including expressions for the crossover time and the maximum temperature difference. We also discuss the limitations of our linearized theory., 13 pages, 6 figures; v2: subfigures for the evolution of $a_2$ added, plus other minor changes. Special issue in memory of Prof. Jason Reese

Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation., Main text: 5 pages; 18 pages with appendices and references; major revision with results for a general non-linear potential and study of fluctuations added; Physical Review E in press

We analyse the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the non-equilibrium steady state reached by the system. Here, we investigate two specific situations. First, we look into the ``direct'' relaxation of the system after a single (small) jump of the driving intensity. This study is carried out by two different methods. Not only do we linearise the evolution equations around the steady state, but also derive generalised out-of-equilibrium fluctuation-dissipation relations for the relevant response functions. Second, we investigate the behaviour of the system in a more complex experiment, specifically a Kovacs-like protocol with two jumps in the driving. The emergence of anomalous Kovacs response is explained in terms of the properties of the direct relaxation function: it is the second mode changing sign at the critical value of the inelasticity that demarcates anomalous from normal behaviour. The analytical results are compared with numerical simulations of the kinetic equation, and a good agreement is found., Comment: 14 pages, 10 figures; major revision; completely new section on non-equilibrium FDR; accepted for publication in PRE

We consider the problem of building a continuous stochastic model, i.e., a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom of the “bath” to which the particle is coupled. Specifically, we look into the general case where the bath may be at negative temperatures, as found, for instance, in models and experiments with bounded effective kinetic energy. Here, we generalize previous studies by considering the case in which the coarse graining leads to (i) a renormalization of the potential felt by the particle, and (ii) spatially dependent viscosity and diffusivity. In addition, a particular relevant example is provided, where the bath is a spin system and a sort of phase transition takes place when going from positive to negative temperatures. A Chapman-Enskog-like expansion allows us to rigorously derive the Fokker-Planck equation from the microscopic dynamics. Our theoretical predictions show excellent agreement with numerical simulations

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data., v2: 6 pages, 4 figures, major revision, Rapid Communication in PRE

We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness $\kappa$. We work out the optimal time dependence $\kappa(t)$ by minimising the work performed on the particle under the non-holonomic constraint $0\leq\kappa\leq\kappa_{\max}$, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analysed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time $t_{\text{f}}$ and the desired compression ratio $\kappa_{\text{f}}/\kappa_{\text{\i}}$, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimisation of heat engines., Comment: 16 pages, 9 figures; submitted to Physical Review E

We investigate a lattice model representing a granular gas in a thin channel. We deduce the hydrodynamic description for the model from the microscopic dynamics in the large system limit, including the lowest finite-size corrections. The main prediction from hydrodynamics, when finite-size corrections are neglected, is the existence of a steady "uniform longitudinal flow" (ULF), with the granular temperature and the velocity gradient both uniform and directly related. Extensive numerical simulations of the system show that such a state can be observed in the bulk of a finite-size system by attaching two thermostats with the same temperature at its boundaries. The relation between the ULF state and the shocks appearing in the late stage of a cooling gas of inelastic hard rods is discussed., 12 pages, 6 figures, to be published on Physical Review E (in press)

We analyse the unfolding pathway of biomolecules comprising several independent modules in pulling experiments. In a recently proposed model, a critical velocity \(v_{c}\) has been predicted, such that for pulling speeds \(v>v_{c}\) it is the module at the pulled end that opens first, whereas for \(v

A theoretical analysis of the unfolding pathway of simple modular proteins in length- controlled pulling experiments is put forward. Within this framework, we predict the first module to unfold in a chain of identical units, emphasizing the ranges of pulling speeds in which we expect our theory to hold. These theoretical predictions are checked by means of steered molecular dynamics of a simple construct, specifically a chain composed of two coiled-coils motives, where anisotropic features are revealed. These simulations also allow us to give an estimate for the range of pulling velocities in which our theoretical approach is valid., Comment: Accepted for publication in J. Chem. Theory Comput.; only one PDF file with the main text and the supporting information (generated from a docx file)

In kinetic theory, a system is usually described by its one-particle distribution function $f(\mathbf{r},\mathbf{v},t)$, such that $f(\mathbf{r},\mathbf{v},t)d\mathbf{r} d\mathbf{v}$ is the fraction of particles with positions and velocities in the intervals $(\mathbf{r}, \mathbf{r}+d\mathbf{r})$ and $(\mathbf{v}, \mathbf{v}+d\mathbf{v})$, respectively. Therein, global stability and the possible existence of an associated Lyapunov function or $H$-theorem are open problems when non-conservative interactions are present, as in granular fluids. Here, we address this issue in the framework of a lattice model for granular-like velocity fields. For a quite general driving mechanism, including both boundary and bulk driving, we show that the steady state reached by the system in the long time limit is globally stable. This is done by proving analytically that a certain $H$-functional is non-increasing in the long time limit. Moreover, for two specific energy injection mechanisms, we are able to demonstrate that the proposed $H$-functional is non-increasing for all times. Also, we put forward a proof that clearly illustrates why the "classical" Boltzmann functional $H_{B}[f]=\int\! d\mathbf{r} \, d\mathbf{v} f(\mathbf{r},\mathbf{v},t) \ln f(\mathbf{r},\mathbf{v},t)$ is inadequate for systems with non-conservative interactions. Not only is this done for the simplified kinetic description that holds in the lattice models analysed here but also for a general kinetic equation, like Boltzmann's or Enskog's., Comment: 13 pages, 5 figures; minor revision, accepted for publication in PRE

Control of cooling and heating processes is essential in many industrial and biological processes. In fact, the time evolution of an observable quantity may differ according to the previous history of the system. For example, a system that is being subject to cooling and then, at a given time $t_{w}$ for which the instantaneous temperature is $T(t_w)=T_{\mathrm{st}}$, is suddenly put in contact with a temperature source at $T_{\mathrm{st}}$ may continue cooling down temporarily or, on the contrary, undergo a temperature rebound. According to current knowledge, there can be only one "spurious" and small peak/low. However, our results prove that, under certain conditions, more than one extremum may appear. Specifically, we have observed regions with two extrema and a critical point with three extrema. We have also detected cases where extraordinarily large extrema are observed, as large as the order of magnitude of the stationary value of the variable of interest. We show this by studying the thermal evolution of a low density set of macroscopic particles that do not preserve kinetic energy upon collision, i.e., a granular gas. We describe the mechanism that signals in this system the emergence of these complex and large memory effects, and explain why similar observations can be expected in a variety of systems., 15 pages, 5 figures

Under certain conditions, two samples of fluid at different initial temperatures present a counterintuitive behavior known as the Mpemba effect: it is the hotter system that cools sooner. Here, we show that the Mpemba effect is present in granular fluids, both in uniformly heated and in freely cooling systems. In both cases, the system remains homogeneous, and no phase transition is present. Analytical quantitative predictions are given for how differently the system must be initially prepared to observe the Mpemba effect, the theoretical predictions being confirmed by both molecular dynamics and Monte Carlo simulations. Possible implications of our analysis for other systems are also discussed., 6 pages, 4 figures; v2: molecular dynamics results added

A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but dissipate energy. The dynamics can be described by a stochastic equation in full phase space, or through the corresponding Master Equation for the time evolution of the probability distribution. In the hydrodynamic limit, equations for the average velocity and temperature fields with fluctuating currents are derived, which are analogous to those of granular fluids when restricted to the shear modes. Therefore, the homogeneous cooling state, with its linear instability, and other relevant regimes such as the uniform shear flow and the Couette flow states are described. The evolution in time and space of the single particle probability distribution, in all those regimes, is also discussed, showing that the local equilibrium is not valid in general. The noise for the momentum and energy currents, which are correlated, are white and Gaussian. The same is true for the noise of the energy sink, which is usually negligible.

Motivational interviewing (MI) is a collaborative, goal-oriented method to help patients change behaviour. Tools that are often used to measure MI are the motivational interviewing skills code' (MISC), the 'motivational interviewing treatment integrity' (MITI) and the 'behaviour change counselling index' (BECCI). The first two instruments have not been designed to be used in primary healthcare (PHC) settings. The BECCI actually is time-consuming. The motivational interviewing assessment scale (MIAS, 'EVEM' in Spanish) was developed to measure MI in PHC encounters as an alternative to the previous instruments.To validate MIAS as an instrument to assess the quality of MI in PHC settings.(a)Sixteen experts in MI participated in the design, face and consensus validity, using a Delphi-type methodology. (b)27 PHC centres located in Spain.four experts in MI tested its psychometric properties with 332 video recordings coming from the Dislip-EM study (consultations provided by 37 practitioners).dimensionality, internal consistency, reliability (intra-class correlation coefficient-ICC), sensitivity to change and convergent validity with the BECCI scale.A 14-item scale was obtained after the validation process. Factor analysis: two factors explained 76.6% of the total variance. Internal consistency, α = 0.99. Reliability: intra-rater ICC = 0.96; inter-rater ICC = 0.97. Sensitivity to change: means before and after training were 23.63 versus 38.57 (P 0.001). Spearman's coefficient between the MIAS and the BECCI scale was 0.98 (P 0.001).The MIAS is a consistent and reliable instrument to assess the use of MI in PHC settings. [Box: see text].

Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest-neighbour inelastic collisions that conserve momentum but dissipate energy. A set of equations for the fluctuating hydrodynamics of the velocity and energy mesoscopic fields give a first approximation for (i) the velocity structure factor and (ii) the finite-size correction to the Haff law, both in the homogeneous cooling regime. At a more refined level, we have derived the equations for the two-site velocity correlations and the total energy fluctuations. First, we seek a perturbative solution thereof, in powers of the inverse of system size. On the one hand, when scaled with the granular temperature, the velocity correlations tend to a stationary value in the long time limit. On the other hand, the scaled standard deviation of the total energy diverges, that is, the system shows multiscaling. Second, we find an exact solution for the velocity correlations in terms of the spectrum of eigenvalues of a certain matrix. The results of numerical simulations of the microscopic model confirm our theoretical results, including the above described multiscaling phenomenon.

We consider a simple spin-membrane model for rippling in graphene. The model exhibits transitions from a flat but rippled membrane to a buckled one. At high temperature the transition is second order but it is first order at low temperature for appropriate strength of the spin-spin coupling. Driving the system across the first order phase transition in nonequilibrium conditions that mimic interaction of the graphene membrane with a STM tip explains recent experiments. In particular, we observe a reversible behavior for small values of the STM current and an irreversible transition from flat rippled membrane to rigid buckled membrane when the current surpasses a critical value. This work opens the possibility to test mechanical properties of graphene under different temperature and electrostatic conditions., Comment: 20 pages, 8 figures

By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and explicit expressions for the average and the variance are provided. Experimental and molecular dynamics results are analyzed and qualitatively compared with the model predictions. The relevance of considering open or closed systems is discussed, as well as the meaning and properties of the Edwards compactivity and the effective (configurational) temperature introduced by some authors. Finally, the linear response to a change in the vibration intensity is also investigated. A KWW decay of the volume response function is clearly identified. This seems to confirm some kind of similarity between externally excited granular systems and structural glasses., Comment: 23 pages, 5 figures; accepted version in Powder Technology, Special Issue on Granular Temperature

ObjetivosConocer las opiniones de los profesionales de atención primaria sobre las actividades preventivas en la práctica clínica, así como los obstáculos percibidos por los profesionales para realizarlas y las posibles formas de superarlos.ParticipantesEn total participaron 129 profesionales, entre los que se incluían médicos de atención primaria, profesionales de enfermería, técnicos y responsables de gestión de servicios de atención primaria, y profesionales de salud pública.DiseñoCuestionario Delphi enviado por correo electrónico.EmplazamientoAtención primaria en Cataluña.Mediciones y resultados principalesSe realizaron dos rondas en las que se obtuvieron tasas de respuesta del 48,9 y el 67,4%, respectivamente. Tras la segunda ronda se obtuvo una convergencia superior al 40% en todas las preguntas. Los principales problemas para la prevención en la práctica fueron la falta de tiempo, la falta de formación y las propias actitudes de los profesionales hacia la prevención. Para mejorar la implementación de la prevención en la práctica, los profesionales señalaron la formación en habilidades de comunicación, metodología del consejo y la utilización de guías de práctica clínica.ConclusionesLos profesionales apuntan algunas necesidades específicas en la formación que pueden contribuir a mejorar la integración de las actividades preventivas. Por otro lado, se detecta la necesidad de mejorar las actitudes de los propios profesionales hacia la prevención.ObjectivesTo find out the opinions of primary care professionals on prevention activities in clinical practice, as well as the perceived obstacles to carrying them out and ways of overcoming them.ParticipantsA total of 129 professionals participated, including primary care doctors, nurses, technicians, primary care service managers, and public health professionals.DesignDelphi questionnaire sent by e-mail.SettingPrimary care in Catalonia, Spain.Main measurements and resultsTwo rounds were made with response rates of 48.9% and 67.4%, respectively. Convergence of over 40% was obtained in all the questions after the second round. The main problems for prevention in clinical practice were lack of time, lack of training and the attitudes of the professionals themselves towards prevention. To improve implementing prevention in the practice, the professionals pointed out, training in communication skills, advice methodology and the use of clinical practice guidelines.ConclusionsHealth professionals pointed out some specific needs in training which could help to improve the inclusion of prevention activities.On the other hand, it was noted that the attitudes of the professionals themselves towards prevention need to be improved.

Background It is known that making people change their habits is challenging. It is crucial to identify the most effective approach that general practitioners (GPs) should use to help their patients change unhealthy habits. The objective this study was to assess the efficacy of a multifactorial intervention based on Motivational Interviewing performed by general practitioners to enhance lipid levels in patients with dyslipidemia, as compared to standard care. Methods A multicenter, controlled, randomized, cluster, two-parallel arm trial with a 12-month follow-up conducted in 25 community health centers of the Spanish. 38 GPs and 227 primary care patients with uncontrolled dyslipidemia were included in the trial. GPs performed an intervention based either on Motivational Interviewing (MI) or standard practice. Lipid levels were measured, and the control degree was analyzed based on the criteria of clinical guidelines. Results 107 were assigned to the Experimental Group (EG) and 120 to the Control Group (CG). An overall improvement was achieved in total cholesterol levels (Mean Difference –MD- = −19.60; 95 % CI: −15.33 at −23.87 mg/dl; p

Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the non-equilibrium behaviour of the system of interest; their statistics, associated structures and microscopic origin. During the last years, some new general and powerful methods have appeared to delve into fluctuating behaviour that have drastically changed the way to address this problem in the realm of diffusive systems: macroscopic fluctuation theory (MFT) and a set of advanced computational techniques that make it possible to measure the probability of rare events. Notwithstanding, a satisfactory theory is still lacking in a particular case of intrinsically non-equilibrium systems, namely those in which energy is not conserved but dissipated continuously in the bulk of the system (e.g. granular media). In this work, we put forward the dissipated energy as a relevant quantity in this case and analyse in a pedagogical way its fluctuations, by making use of a suitable generalisation of macroscopic fluctuation theory to driven dissipative media., Comment: 22 pages, 3 figures

We study a model describing the force-extension curves of modular proteins, nucleic acids, and other biomolecules made out of several single units or modules. At a mesoscopic level of description, the configuration of the system is given by the elongations of each of the units. The system free energy includes a double-well potential for each unit and an elastic nearest neighbor interaction between them. Minimizing the free energy yields the system equilibrium properties whereas its dynamics is given by (overdamped) Langevin equations for the elongations, in which friction and noise amplitude are related by the fluctuation-dissipation theorem. Our results, both for the equilibrium and the dynamical situations, include analytical and numerical descriptions of the system force-extension curves under force or length control, and agree very well with actual experiments in biomolecules. Our conclusions also apply to other physical systems comprising a number of metastable units, such as storage systems or semiconductor superlattices., major revision, accepted for publication in PRE; 20 pages, 13 figures

A system of atoms connected by harmonic springs to their nearest neighbors on a lattice is coupled to Ising spins that are in contact with a thermal bath and evolve under Glauber dynamics. Assuming a nearest-neighbor antiferromagnetic interaction between spins, we calculate analytically the equilibrium state. On a one-dimensional attice, the system exhibits first and second order phase transitions. The order parameters are the total magnetization and the number of spin pairs in an antiferromagnetic configuration. On a hexagonal two dimensional lattice, spins interact with their nearest-neighbors and next-nearest-neighbors. Together with the coupling to atoms, these interactions produce a complex behavior that is displayed on a phase diagram. There are: ordered phases associated to ripples with atomic wavelength and antiferromagnetic order, ordered phases associated to ripples with nanometer wavelengths and ferromagnetic order, disordered glassy phases, and other phases presenting stripes formed by different domains. These static phases are discussed in relation to existing experiments and results for other models found in the literature., accepted for publication in JSTAT

The dependence of the unfolding pathway of proteins on the pulling speed is investigated. This is done by introducing a simple one-dimensional chain comprising $N$ units, with different characteristic bistable free energies. These units represent either each of the modules in a modular protein or each of the intermediate "unfoldons" in a protein domain, which can be either folded or unfolded. The system is pulled by applying a force to the last unit of the chain, and the units unravel following a preferred sequence. We show that the unfolding sequence strongly depends on the pulling velocity $v_{p}$. In the simplest situation, there appears a critical pulling speed $v_{c}$: for pulling speeds $v_{p}v_{c}$ it is the pulled unit that unfolds first. By means of a perturbative expansion, we find quite an accurate expression for this critical velocity., Comment: accepted for publication in JSTAT

We introduce a model described in terms of a scalar velocity field on a 1d lattice, evolving through collisions that conserve momentum but do not conserve energy. Such a system posseses some of the main ingredients of fluidized granular media and naturally models them. We deduce non-linear fluctuating hydrodynamics equations for the macroscopic velocity and temperature fields, which replicate the hydrody- namics of shear modes in a granular fluid. Moreover, this Landau-like fluctuating hydrodynamics predicts an essential part of the peculiar behaviour of granular flu- ids, like the instability of homogeneous cooling state at large size or inelasticity. We compute also the exact shape of long range spatial correlations which, even far from the instability, have the physical consequence of noticeably modifying the cooling rate. This effect, which stems from momentum conservation, has not been previously reported in the realm of granular fluids., Comment: 16 pages, 6 figures

It is analytically shown that the one-dimensional Ising model with Glauber dynamics exhibits short time memory effects when submitted to an abrupt change in the temperature. These effects are qualitatively similar to those experimentally observed in the compaction of vibrated granular materials. Moreover, a critical time separating regimes of ``normal'' and ``anomalous'' responses to the perturbation is found., Comment: 7 pages, 2 figures; accepted (revised) version, to appear in Europhysics Letters

While memory effects have been reported for dense enough disordered systems such as glasses, we show here by a combination of analytical and simulation techniques that they are also intrinsic to the dynamics of dilute granular gases. By means of a certain driving protocol, we prepare the gas in a state where the granular temperature $T$ coincides with its long time limit. However, $T$ does not subsequently remain constant, but exhibits a non-monotonic evolution before reaching its non-equilibrium steady value. The corresponding so-called Kovacs hump displays a normal behavior for weak dissipation (as observed in molecular systems), but is reversed under strong dissipation, where it thus becomes anomalous., 5 pages, to appear in Physical Review Letters

We evidence a Kovacs-like memory effect in a uniformly driven granular gas. A system of inelastic hard particles, in the low density limit, can reach a nonequilibrium steady state when properly forced. By following a certain protocol for the drive time dependence, we prepare the gas in a state where the granular temperature coincides with its long time value. The temperature subsequently does not remain constant but exhibits a nonmonotonic evolution with either a maximum or a minimum, depending on the dissipation and on the protocol. We present a theoretical analysis of this memory effect at Boltzmann-Fokker-Planck equation level and show that when dissipation exceeds a threshold, the response can be called anomalous. We find excellent agreement between the analytical predictions and direct Monte Carlo simulations. España Ministerio de Educación, Cultura y Deporte Grant No. PRX12/00362 España Ministerio de Economía y Competitividad Grant No. FIS2011-24460

Single-molecule atomic force spectroscopy probes elastic properties of titin, ubiquitin and other relevant proteins. We explain bioprotein folding dynamics under both length- and force-clamp by modeling polyprotein modules as particles in a bistable potential, weakly connected by harmonic spring linkers. Multistability of equilibrium extensions provides the characteristic sawtooth force-extension curve. We show that abrupt or stepwise unfolding and refolding under force-clamp conditions involve transitions through virtual states (which are quasi-stationary domain configurations) modified by thermal noise. These predictions agree with experimental observations., 6 pages, accepted for publication in EPL http://iopscience.iop.org/epl

The one-dimensional Ising model with nearest neighbour interactions and the zero-temperature dynamics recently considered by Lefevre and Dean -J. Phys. A: Math. Gen. {\bf 34}, L213 (2001)- is investigated. By introducing a particle-hole description, in which the holes are associated to the domain walls of the Ising model, an analytical solution is obtained. The result for the asymptotic energy agrees with that found in the mean field approximation., 6 pages, no figures; accepted in J. Phys. A: Math. Gen. (Letter to the Editor)

A simple model for the dynamics of a granular system under tapping is studied. The model can be considered as a particularization for short taps of a more general one-dimensional lattice model with facilitated dynamics. The steady state reached by the system is discussed and the results are shown to be consistent with the thermodynamic granular theory developed by Edwards and coworkers. In particular, the basic assumption of the theory, i.e., that the probability distribution depends only on the volume of the configuration, is verified.

A simple lattice model is used to study compaction in granular media. As in real experiments, we consider a series of taps separated by large enough waiting times. The relaxation of the density exhibits the characteristic inverse logarithmic law. Moreover, we have been able to identify analytically the relevant time scale, leading to a relaxation law independent of the specific values of the parameters. Also, an expression for the asymptotic density reached in the compaction process has been derived. The theoretical predictions agree fairly well with the results from the Monte Carlo simulation., 15 pages, 4 figures, REVTeX file; no changes except for single-spacing to save paper (previous version 22 pages)

A Monte Carlo algorithm for simulating master equations with time-dependent transition rates is described. It is based on a waiting time image, and takes into account that the system can become frozen when the transition rates tend to zero fast enough in time. An analytical justification is provided. The algorithm reduces to the Bortz-Kalos-Lebowitz one when the transition rates are constant. Since the exact evaluation of waiting times is rather involved in general, a simple and efficient iterative method for accurately calculating them is introduced. As an example, the algorithm is applied to a one-dimensional Ising system with Glauber dynamics. It is shown that it reproduces the exact analytical results, being more efficient than the direct implementation of the Metropolis algorithm

We study the dynamical behavior of a system with a variable number of particles n. The empty state n=0 is the ground state, while all the other states n>0 are degenerate in energy. In equilibrium, the mean number of particles is equal to unity, independently of the temperature. The static properties are the same as for the Backgammon model recently proposed by Ritort [Phys. Rev. Lett. 75, 1190 (1995)], while a variation of the kinetics is considered. The elementary dynamical processes are the arrival and departure of a particle. The rate of the departure process is constant, while the arrival rate is obtained from the detailed balance condition. Thus, there is no energy barrier separating the ground state n=0. Nevertheless, glassy behavior appears due to the presence of effective entropy barriers. At low temperatures, the response functions are shown to obey φ(t)≃exp[-(t/τ)γ]. In thermal cycles of cooling and reheating from low temperatures, the system shows hysteresis, which follows from the trend of the system to approach the normal curve characterizing the heating program. Dirección General de Investigación Científica y Técnica (Spain) through Grant No. PB96-0534.

We analyze the so-called Kovacs effect in the one-dimensional Ising model with Glauber dynamics. We consider small enough temperature jumps, for which a linear response theory has been recently derived. Within this theory, the Kovacs hump is directly related to the monotonic relaxation function of the energy. The analytical results are compared with extensive Monte Carlo simulations, and an excellent agreement is found. Remarkably, the position of the maximum in the Kovacs hump depends on the fact that the true asymptotic behavior of the relaxation function is different from the stretched exponential describing the relevant part of the relaxation at low temperatures., accepted for publication in Phys. Rev. E

We analyze the force-extension curve for a general class of systems, which are described at the mesoscopic level by a free energy depending on the extension of its components. Similarly to what is done in real experiments, the total length of the system is the controlled parameter. This imposes a global constraint in the minimization procedure leading to the equilibrium values of the extensions. As a consequence, the force-extension curve has multiple branches in a certain range of forces. The stability of these branches is governed by the free energy: there are a series of first-order phase transitions at certain values of the total length, in which the free energy itself is continuous but its first derivative, the force, has a finite jump. This behavior is completely similar to that observed in real experiments with biomolecules like proteins and with other complex systems España Ministerio de Economía y Competitividad Grants No. FIS2011- 24460 (A.P.), No. FIS2011-28838-C02-01

We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated to a path in mesoscopic phase-space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in non-dissipative systems. This is a consequence of the quasi-elasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always gaussian, as expected from the central limit theorem. On the other hand, strong separation from the gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily supressed in the latter. (...) [see complete abstract by downloading the paper], Comment: 24 pages

The stochastic resonance phenomenon for a one-dimensional Ising model in an oscillating magnetic field is discussed. Within the linear field approximation, the amplitude of the induced magnetization presents a maximum as a function of the temperature. The behaviour of the phase shift is also studied.

The decay of the spin-spin time correlation functions in a one-dimensional Ising model with Glauber dynamics is studied. In the low-temperature limit, an asymptotically valid continuous space equation is derived. It is a modified diffusion equation with a purely exponential relaxation term. Its solution leads to an exact Cole-Davison behavior of the spin autocorrelation in the frequency domain, while in the time description a KWW function followed by an exponential decay is obtained. The exponent of the KWW, analytically derived, is 1/2, and not 0.63, as has been reported in the literature. España Direccion General de Investigacion Cientifica y Tecnica through Grant No. PB92-0683

We comment on the paper "Critique and correction of the currently accepted solution of the infinite spherical well in quantum mechanics" by Huang Young-Sea and Thomann Hans-Rudolph, EPL 115, 60001 (2016) ., Comment: 2 pages; Submitted to the Comments Section of EPL