We discuss the Sherrington-Kirkpatrick mean-field version of a spin glass within the distributional zeta function method (DZFM). In the DZFM, since the dominant contribution to the average free energy is written as a series of moments of the partition function of the model, the spin-glass multivalley structure is obtained. Also, an exact expression for the saddle points corresponding to each valley and a global critical temperature showing the existence of many stables or at least metastable equilibrium states is presented. Near the critical point, we obtain analytical expressions of the order parameters that are in agreement with phenomenological results. We evaluate the linear and nonlinear susceptibility and we find the expected singular behavior at the spin-glass critical temperature. Furthermore, we obtain a positive definite expression for the entropy and we show that ground-state entropy tends to zero as the temperature goes to zero. We show that our solution is stable for each term in the expansion. Finally, we analyze the behavior of the overlap distribution, where we find a general expression for each moment of the partition function.

Surface growth properties during irreversible multilayer deposition of straight semirigid rods on linear and square lattices have been studied by Monte Carlo simulations and analytical considerations. The filling of the lattice is carried out following a generalized random sequential adsorption mechanism where the depositing objects can be adsorbed on the surface forming multilayers. The results of our simulations show that the roughness evolves in time following two different behaviors: an “homogeneous growth regime” at initial times, where the heights of the columns homogeneously increase, and a “segmented growth regime” at long times, where the adsorbed phase is segmented in actively growing columns and inactive nongrowing sites. Under these conditions, the surface growth generated by the deposition of particles of different sizes is studied. At long times, the roughness of the systems increases linearly with time, with growth exponent $\beta =1$, at variance with a random deposition of monomers which presents a sublinear behavior ($\beta =1/2$). The linear behavior is due to the segmented growth process, as we show using a simple analytical model.

We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen. We devise a parsimonious method for selecting the optimal control parameters, without requiring any Monte Carlo simulations of the system. This method relies on a new nonlinear Fokker-Planck equation whose stationary response distribution is approximated by a rapidly convergent iterative algorithm. In addition, our framework allows us to accurately predict, and subsequently suppress, the modal drift and tail inflation in the controlled stationary distribution. We demonstrate the efficacy of our method on two examples, including an optical laser model perturbed by multiplicative colored noise.

Bacterial persistence, tolerance to antibiotics via stochastic phenotype switching, provides a survival strategy and a fitness advantage in temporally fluctuating environments. Here we study its possible benefit in spatially varying environments using a Fisher wave approach. We study the spatial expansion of a population with stochastic switching between two phenotypes in spatially homogeneous conditions and in the presence of an antibiotic barrier. Our analytical results show that the expansion speed in growth-supporting conditions depends on the fraction of persister cells at the leading edge of the population wave. The leading edge contains a small fraction of persister cells, keeping the effect on the expansion speed minimal. The fraction of persisters increases gradually in the interior of the wave. This persister pool benefits the population when it is stalled by an antibiotic environment. In that case, the presence of persister enables the population to spread deeper into the antibiotic region and to cross an antibiotic region more rapidly. Further we observe that optimal switching rates maximize the expansion speed of the population in spatially varying environments with alternating regions of growth permitting conditions and antibiotics. Overall, our results show that stochastic switching can promote population expansion in the presence of antibiotic barriers or other stressful environments.

We study the influence of solid boundaries on dynamics and structure of kinesin-driven microtubule active fluids as the height of the container, $H$, increases from hundreds of micrometers to several millimeters. By three-dimensional tracking of passive tracers dispersed in the active fluid, we observe that the activity level, characterized by velocity fluctuations, increases as system size increases and retains a small-scale isotropy. Concomitantly, as the confinement level decreases, the velocity-velocity temporal correlation develops a strong positive correlation at longer times, suggesting the establishment of a “memory”. We estimate the characteristic size of the flow structures from the spatial correlation function and find that, as the confinement becomes weaker, the correlation length, $l_c$, saturates at approximately 400 microns. This saturation suggests an intrinsic length scale which, along with the small-scale isotropy, demonstrates the multiscale nature of this kinesin-driven bundled microtubule active system.

Fluctuation theorems allow one to obtain equilibrium information from nonequilibrium experiments. The probability distribution function of the relevant magnitude measured along the irreversible nonequilibrium trajectories is an essential ingredient of fluctuation theorems. In small systems, where fluctuations can be larger than average values, probability distribution functions often deviate from being Gaussian, showing long tails, mostly exponential, and usually strongly asymmetric. Recently, the probability distribution function of the van Hove correlation function of the relevant magnitude was calculated, instead of that of the magnitude itself. The resulting probability distribution function is highly symmetric, obscuring the application of fluctuation theorems. Here, the discussion is illustrated with the help of results for the heat exchanged during plastic deformation of aluminum nanowires, obtained from molecular dynamics calculations. We find that the probability distribution function for the heat exchanged is centrally Gaussian, with asymmetric exponential tails further out. By calculating the symmetry function we show that this distribution is consistent with fluctuation theorems relating the differences between two equilibrium states to an infinite number of nonequilibrium paths connecting those two states.

Recent experiments have shown that a deep neural network can be trained to predict the action of $t$ steps of Conway's Game of Life automaton given millions of examples of this action on random initial states. However, training was never completely successful for $t>1$, and even when successful, a reconstruction of the elementary rule ($t=1$) from $t>1$ data is not within the scope of what the neural network can deliver. We describe an alternative network-like method, based on constraint projections, where this is possible. From a single data item this method perfectly reconstructs not just the automaton rule but also the states in the time steps it did not see. For a unique reconstruction, the size of the initial state need only be large enough that it and the $t-1$ states it evolves into contain all possible automaton input patterns. We demonstrate the method on 1D binary cellular automata that take inputs from $n$ adjacent cells. The unknown rules in our experiments are not restricted to simple rules derived from a few linear functions on the inputs (as in Game of Life), but include all $2^{2^n}$ possible rules on $n$ inputs. Our results extend to $n=6$, for which exhaustive rule-search is not feasible. By relaxing translational symmetry in space and also time, our method is attractive as a platform for the learning of binary data, since the discreteness of the variables does not pose the same challenge it does for gradient-based methods.

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature: one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related to the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.

The instabilities of the steady axisymmetric thermocapillary-buoyancy flow in a rotating annular pool were investigated by linear stability analysis. The critical instability parameters for the thermocapillary-buoyancy flow (normal gravity) and the pure thermocapillary flow (microgravity) were compared under different pool depths and rotation rates. The results show that the thermocapillary-buoyancy flow is more stable than the pure thermocapillary flow due to the stabilizing effect of the gravity (buoyancy) force. Two types of oscillatory instabilities were observed depending on the different rotation rates, and the propagation direction of the hydrothermal wave is also affected by the rotation rate.

Inspired by recent experimental work on virus-polymer mixtures, we study the properties of thin smectic fibrils composed of chiral rodlike particles using Monte Carlo simulations. Due to the interplay between surface energy, elastic deformation energy, and entropic effects, the fibril's layers relax into a twisted state. We focus our study on the layers' twist direction and map our results to the antiferromagnetic Ising model. In this view, the chiral interaction mimics an external field that drives the layers to have the same sense of twist. Besides, we determine the free energy difference and barrier height between an alternating and a nonalternating sequence of twisted layers composed of achiral rods and find that an alternating sequence is slightly preferred. We also see that the fibrils contract on increasing the chiral interaction strength and think that further studies on self-assembled functional materials can use our results.

Microscopic details of buckling-induced topological defects are required for molecular design of smectic liquid crystals to control buckling instability of the layers. In this study, we present a multiobjective optimization method to derive the coarse-grained (CG) force fields with sufficiently precise buckling characteristics including the molecular details for molecular dynamics (MD) simulations. We perform CGMD simulations of buckling deformation at sample points in the CG force field parameter space, from which the response surfaces of objective functions such as the scalar orientational order parameters, critical angles of layer collapse, and radial distribution functions are estimated. Since not all objective functions can be optimized simultaneously, we use a genetic algorithm to calculate the Pareto set of optimal solutions. We select the models with different molecular head-tail symmetries to study buckling deformation. The extracted CG model successfully reproduces the buckling deformation in terms of the collapse of smectic layers through the generation of dislocations with dipole disclinations. We also find that the molecular symmetry is a dominant factor to control the class of the buckling-induced dislocations.

Amorphous solids yield at a critical value ${\mathrm{\Sigma }}_c$ of the imposed stress $\mathrm{\Sigma }$ through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow even below ${\mathrm{\Sigma }}_c$. Here we study the steady-state thermal flow of amorphous solids using a mesoscopic elastoplastic model. In the Hébraud-Lequex (HL) model we provide an analytical solution of the thermally activated flow at low temperature. We then propose a general scaling law that also describes the transition rounding. Finally, we find that the scaling law holds in numerical simulations of the HL model, a two-dimensional (2D) elastoplastic model, and previously published molecular dynamics simulations of 2D Lennard-Jones glass.

We study the connection between the magnetization profiles of models described by a scalar field with marginal interaction term in a bounded domain and the solutions of the so-called Yamabe problem in the same domain, which amounts to finding a metric having constant curvature. Taking the slab as a reference domain, we first study the magnetization profiles at the upper critical dimensions $d=3$, 4, 6 for different (scale-invariant) boundary conditions. By studying the saddle-point equations for the magnetization, we find general formulas in terms of Weierstrass elliptic functions, extending exact results known in literature and finding ones for the case of percolation. The zeros and poles of the Weierstrass elliptic solutions can be put in direct connection with the boundary conditions. We then show that, for any dimension $d$, the magnetization profiles are solution of the corresponding integer Yamabe equation at the same $d$ and with the same boundary conditions. The magnetization profiles in the specific case of the four-dimensional Ising model with fixed boundary conditions are compared with Monte Carlo simulations, finding good agreement. These results explicitly confirm at the upper critical dimension recent results presented in Gori and Trombettoni [J. Stat. Mech: Theory Exp. (2020) 063210].

In this paper, the impact of temperature fluctuations in the entanglement of two qubits described by a spin-1/2 $XX$ model is studied. To describe the out-of-equilibrium situation, superstatistics is used with fluctuations given by a ${\chi }^2$-distribution function, and its free parameters are chosen in such a way that resembles the nonadditive Tsallis thermodynamics. In order to preserve the Legendre structure of the thermal functions, particular energy constraints are imposed on the density operator and the internal energy. Analytical results are obtained using an additional set of constraints after a parametrization of the physical temperature. We show that the well-known parametrization may lead to undesirable values of the physical temperature so that by analyzing the entropy as a function of energy, the correct values are found. The quantum entanglement is obtained from the concurrence and is compared with the case when the Tsallis restrictions are not imposed on the density operator.

We investigate the effect of coarse graining on the thermodynamic properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a sinusoidal potential and driven out of equilibrium by a small constant force. Different levels of coarse graining are evaluated: At first, we compare the results in the underdamped dynamics with those in the overdamped one (first coarse graining). For large values of the friction coefficient, the two dynamics have the same thermodynamics properties, while, for smaller friction values, the overdamped approximation produces an excess of entropy production with respect to that of the underdamped dynamics. Moreover, for further smaller values of the drag coefficient, the excess of entropy production turns into a loss. These regimes are explained by evaluating the jump statistics, observing that the inertia is able to induce multiple jumps and affect the average jump rate. The periodic shape of the potential allows us to approximate the continuous dynamics via a Markov chain after the introduction of a suitable time and space discretization (second level of coarse graining). This discretization procedure is implemented starting both from the underdamped and the overdamped evolution and is analyzed for different values of the friction coefficient.

We investigate delay-time distributions in the scattering of short Gaussian pulses in microwave networks which simulate quantum graphs. We show that in the limit of short delay times the delay-time distribution is very sensitive to the internal structure of the networks. Therefore, it can be used to reveal their local structure including the boundary conditions at the vertices of the networks. In the frequency domain the pulses comprise many resonance frequencies of the networks. Furthermore, we show that the time-delay distribution averaged over different internal configurations of a finite network decays exponentially. Our experimental results for four-vertex and isoscattering microwave networks are in very good agreement with the theoretical ones obtained from the modified theory of U. Smilansky and H. Schanz [J. Phys. A 51, 075302 (2018)]. We modified the theory to account for internal absorption of microwave networks.

Directed ratchet transport is generally observed in nonautonomous systems as a result of the interplay of nonlinearity, symmetry breaking, and nonequilibrium fluctuations. Here we demonstrate that ratchet dynamics can appear in significant transporting degrees of freedom of dissipative coupled systems without external bias due to unidirectional coupling of oscillatory degrees of freedom (which are also nonbiasing in any direction), while optimal enhancement of directed ratchet transport occurs when the initial conditions and parameters of such ratcheting degrees of freedom are suitably chosen as predicted by the theory of ratchet universality. The simple case of linear oscillatory degrees of freedom is discussed in detail, and numerical experiments are described which confirm all the theoretical predictions, including the dependence of current (velocity) reversals on the initial conditions and the ratcheting degrees-of-freedom parameters. This autonomous ratchet scenario could be exploited technologically, for instance, in the context of noncontact, rack-and-pinion type, nanoscale setups with coupling from the lateral Casimir force, and is relevant for studies of molecular motors in the biological realm.

One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role. Hitherto much theoretical and experimental research has focused on systems composed of passive Brownian particles. In this paper, we study the heat fluctuations in a system of interacting active particles. Specifically we consider a one-dimensional harmonic chain of $N$ active Ornstein-Uhlenbeck particles, with the chain ends connected to heat baths of different temperatures. We compute the moment-generating function for the heat flow in the steady state. We employ our general framework to explicitly compute the moment-generating function for two example single-particle systems. Further, we analytically obtain the scaled cumulants for the heat flow for the chain. Numerical Langevin simulations confirm the long-time analytical expressions for first and second cumulants for the heat flow for a two-particle chain.