We model the time evolution of the mean and the variance of nonstationary time series using the path integral formalism with the purpose to obtain the temporal fluctuation scaling presents in complex systems. To this end, we first show how the probability of change between two times of a stochastic variable can be written in terms of a Feynman kernel, where the cumulant generating function of statistical moments is identified as the Hamiltonian of the system. Thus, by including the effects of a stochastic drift and a temporal logarithmic term in the cumulant generating function, we find analytical expressions describing the temporal evolutions of the mean and the variance in terms of cumulants. Starting from these expressions, we obtain the temporal fluctuation scaling written as a general analytical relation between the variance and the mean, in such a way that this relation satisfies a power law, with the exponent being a function on time. Additionally, we study several financial time series associated with changes of prices for some stock indexes and currencies. For this financial time series, we find that the temporal evolution of the mean and the variance, the temporal fluctuation scaling, and the temporal evolution of the exponent which are obtained from this path integral approach are in agreement with those obtained using the empirical data.

We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected subpopulations. In this setup, oscillators belonging to the same group interact via symmetric couplings while the interaction between subpopulations occurs in an asymmetric fashion. By employing the dimensional reduction scheme of the Ott-Antonsen (OA) theory, we verify the existence of traveling wave and $\pi$-states, in addition to the classical fully synchronized and incoherent states. Bistability between all collective states is reported. Analytical results are generally in excellent agreement with simulations; for some parameters and initial conditions, however, we numerically detect chimera-like states which are not captured by the OA theory.

Nonlinear oscillator systems are ubiquitous in biology and physics, and their control is a practical problem in many experimental systems. Here we study this problem in the context of the two models of spatially coupled oscillators: the complex Ginzburg-Landau equation (CGLE) and a generalization of the CGLE in which oscillators are coupled through an external medium (emCGLE). We focus on external control drives that vary in both space and time. We find that the spatial distribution of the drive signal controls the frequency ranges over which oscillators synchronize to the drive and that boundary conditions strongly influence synchronization to external drives for the CGLE. Our calculations also show that the emCGLE has a low density regime in which a broad range of frequencies can be synchronized for low drive amplitudes. We study the bifurcation structure of these models and find that they are very similar to results for the driven Kuramoto model, a system with no spatial structure. We conclude by discussing qualitative implications of our results for controlling coupled oscillator systems such as the social amoebae Dictyostelium and populations of Belousov Zhabotinsky (BZ) catalytic particles using spatially structured external drives.

Peristalsis by actively generated waves of muscle contraction is one of the most fundamental ways of producing motion in living systems. We show that peristalsis can be modeled by a train of rectangular-shaped solitary waves of localized activity propagating through otherwise passive matter. Our analysis is based on the Fermi-Pasta-Ulam (FPU) type discrete model accounting for active stresses and we reveal the existence in this problem of a critical regime which we argue to be physiologically advantageous.

The brain demands a significant fraction of the energy budget in an organism; in humans, it accounts for 2% of the body mass, but utilizes 20% of the total energy metabolized. This is due to the large load required for information processing; spiking demands from neurons are high but are a key component to understanding brain functioning. Astrocytic brain cells contribute to the healthy functioning of brain circuits by mediating neuronal network energy and facilitating the formation and stabilization of synaptic connectivity. During development, spontaneous activity influences synaptic formation, shaping brain circuit construction, and adverse astrocyte mutations can lead to pathological processes impacting cognitive impairment due to inefficiencies in network spiking activity. We have developed a measure that quantifies information stability within in vitro networks consisting of mixed neural-astrocyte cells. Brain cells were harvested from mice with mutations to a gene associated with the strongest known genetic risk factor for Alzheimer's disease, APOE. We calculate energy states of the networks and using these states, we present an entropy-based measure to assess changes in information stability over time. We show that during development, stability profiles of spontaneous network activity are modified by exogenous astrocytes and that network stability, in terms of the rate of change of entropy, is allele dependent.

To what spatial extent does a single lipid affect the mechanical properties of the membrane that surrounds it? The lipid composition of a membrane determines its mechanical properties. The shapes available to the membrane depend on its compositional material properties, and therefore, the lipid environment. Because each individual lipid species' chemistry is different, it is important to know its range of influence on membrane mechanical properties. This is defined herein as the lipid's mechanical extent. Here, a lipid's mechanical extent is determined by quantifying lipid redistribution and the average curvature that lipid species experience on fluctuating membrane surfaces. A surprising finding is that, unlike unsaturated lipids, saturated lipids have a complicated, nonlocal effect on the surrounding surface, with the interaction strength maximal at a finite length-scale. The methodology provides the means to substantially enrich curvature-energy models of membrane structures, quantifying what was previously only conjecture.

We investigate the void generation and growth process in semicrystalline polymers by large-scale coarse-grained molecular dynamics simulations. Voids are generated in the amorphous layers and grow spherically and then cylindrically, consistent with the results of previous experiments. Interestingly, the fusion of voids is indicated to enlarge the voids in the direction perpendicular to the stretching direction, but not beyond the crystalline layers. The orientational order along the stretching direction increased sharply before void generation, but the increase leveled off afterward. The simulations also clearly reveal that the crystalline layers break but do not bend in the fragmentation process. The dependence of the void growth process on stretching velocity and the stability levels of voids at constant strain are also discussed.

The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency levels belonging to different symmetry classes cross each other and (ii) for levels within the same symmetry sector, only avoided crossings appear. The consequence of anticrossings is studied by calculating the distribution of the ratio of consecutive level spacings for each symmetry class. The resulting ratio distributions disagree with the expected Poissonian result. They are then compared with some well-known transition distributions between Poisson and the Gaussian orthogonal random matrix ensemble. It is found that the distribution of the ratio of consecutive level spacings agrees with the prediction of the Rosenzweig-Porter model. Also, the normal-mode vibration amplitudes are found experimentally on aluminum plates, before and after an avoided crossing for symmetrical-symmetrical, symmetrical-antisymmetrical, and antisymmetrical-symmetrical classes. The measured modes show an excellent agreement with our numerical predictions. The expected Poissonian distribution is recovered for the simply supported rectangular plate.

Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data as well as particle insertions are avoided. Furthermore, no simulations at “uninteresting” state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semigrand canonical ensemble ($\mathrm{NPT}\mathrm{\Delta }\mu$). We describe this Monte Carlo-based Clapeyron integration method, including its basic physical and numerical principles, our extension to electron-ion plasmas, and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense carbon-oxygen plasmas under conditions relevant for the cores of white dwarf stars and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles.

Outer crusts of neutron stars and interiors of cool white dwarfs consist of bare atomic nuclei, arranged in a crystal lattice and immersed in a Fermi gas of degenerate electrons. We study electrostatic properties of such Coulomb crystals, taking into account the polarizability of the electron gas and considering different structures, which can form the ground state: body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal close-packed (hcp), and ${\mathrm{MgB}}_2$-like lattices. At zero temperature the electrostatic energy provides a fundamental contribution to the total energy of the classical Coulomb crystal, which allows us to study structural transitions in the neutron-star crusts and crystallized white-dwarf interiors. To take the electron background polarization into account, we use the linear response theory with the electron dielectric function given either by the Thomas-Fermi approximation or by the random-phase approximation (RPA). We compare the widely used nonrelativistic (Lindhard) version of the RPA with the more general, relativistic (Jancovici) version. The results of the different approximations are compared to assess the importance of going beyond the Thomas-Fermi or Lindhard approximations. We also include the contribution of zero-point vibrations of ions into the ground-state energy. We show that the bcc lattice forms the ground state for any charge number $Z$ of the atomic nuclei at the densities where the electrons are relativistic ($\rho \gtrsim {10}^6\mathrm{g} {\mathrm{cm}}^{-3}$), while at the nonrelativistic densities ($\rho \lesssim {10}^6\mathrm{g} {\mathrm{cm}}^{-3}$) the fcc and hcp lattices can form the ground state. The ${\mathrm{MgB}}_2$-like lattice never forms the ground state at realistic densities in the crystallized regions of degenerate stars. The RPA corrections strongly affect the boundaries between the phases. As a result, transitions between different ground-state structures depend on $Z$ in a nontrivial way. The relativistic and quantum corrections produce less dramatic effects, moderately shifting the phase boundaries.

It is demonstrated that properly reduced transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of Lennard-Jones fluids along isotherms exhibit quasi-universal scaling on the density divided by its value at the freezing point. Moreover, this scaling is closely related to the density scaling of transport coefficients of hard-sphere fluids. The Stokes-Einstein relation without the hydrodynamic diameter is valid in the dense fluid regime. The lower density boundary of its validity can serve as a practical demarcation line between gaslike and liquidlike regimes.

We consider the extended Hubbard diamond chain with an arbitrary number of particles driven by chemical potential. The interaction between dimer diamond chain and nodal couplings is considered in the atomic limit (no hopping), whereas the dimer interaction includes the hopping term. We demonstrate that this model exhibits a pseudo-transition effect in the low-temperature regime. Here, we explore the pseudo-transition rigorously by analyzing several physical quantities. The internal energy and entropy depict sudden, although continuous, jumps which closely resembles discontinuous or first-order phase-transition. At the same time, the correlation length and specific heat exhibit astonishing strong sharp peaks quite similar to a second-order phase-transition. We associate the ascending and descending parts of the peak with power-law “pseudo-critical” exponents. We determine the pseudo-critical exponents in the temperature range where these peaks are developed, namely, $\nu =1$ for the correlation length and $\alpha =3$ for the specific heat. We also study the behavior of the electron density and isothermal compressibility around the pseudo-critical temperature.

We consider the reduced dynamics of a molecular chain weakly coupled to a phonon bath. With a small and constant inhomogeneity in the coupling, the excitation relaxation rates are obtained in closed form. They are dominated by transitions between exciton modes lying next to each other in the energy spectrum. The rates are quadratic in the number of sites in a long chain. Consequently, the evolution of site occupation numbers exhibits longer coherence lifetime for short chains only. When external source and sink are added, the rate equations of exciton occupation numbers are similar to those obtained earlier by Fröhlich to explain energy storage and energy transfer in biological systems. There is a clear separation of timescale into a faster one pertaining to internal influence of the chain and phonon bath, and a slower one determined by external influence, such as the pumping rate of the source, the absorption rate of the sink, and the rate of radiation loss. The energy transfer efficiency at steady state depends strongly on these external parameters and is robust against a change in the internal parameters, such as temperature and inhomogeneity. Excitations are predicted to concentrate to the lowest energy mode when the source power is sufficiently high. In the site basis, this implies that when sustained by a high power source, a sink positioned at the center of the chain is more efficient in trapping energy than a sink placed at its end. Analytic expressions of energy transfer efficiency are obtained in the high power and low-power source limit. Parameters of a photosynthetic system are used as examples to illustrate the results.

Double stranded DNA can adopt different forms, the so-called A-, B-, and Z-DNA, which play different biological roles. In this work, the thermodynamic and the kinetic parameters for the base-pair closing and opening in A-DNA and B-DNA were calculated by all-atom molecular dynamics simulations at different temperatures. The thermodynamic parameters of the base pair in B-DNA were in good agreement with the experimental results. The free energy barrier of breaking a single base stack results from the enthalpy increase $\Delta H$ caused by the disruption of hydrogen bonding and base-stacking interactions, as well as water and base interactions. The free energy barrier of base pair closing comes from the unfavorable entropy loss ΔS caused by the restriction of torsional angles and hydration. It was found that the enthalpy change $\mathrm{\Delta }H$ and the entropy change $\mathrm{\Delta }S$ for the base pair in A-DNA are much larger than those in B-DNA, and the transition rates between the opening and the closing state for the base pair in A-DNA are much slower than those in B-DNA. The large difference of the enthalpy and entropy change for forming the base pair in A-DNA and B-DNA results from different hydration in A-DNA and B-DNA. The hydration pattern observed around DNA is an accompanying process for forming the base pair, rather than a follow-up of the conformation.

Thermodynamic descriptions are powerful tools to formally study complex gene expression programs evolved in living cells on the basis of macromolecular interactions. While transcriptional regulations are often modeled in the equilibrium, other interactions that occur in the cell follow a more complex pattern. Here, we adopt a nonequilibrium thermodynamic scheme to explain the RNA-RNA interaction underlying IS10 transposition. We determine the energy landscape associated with such an interaction at the base-pair resolution, and we present an original scaling law for expression prediction that depends on different free energies characterizing that landscape. Then, we show that massive experimental data of the IS10 RNA-controlled expression are better explained by this thermodynamic description in nonequilibrium. Overall, these results contribute to better comprehend the kinetics of post-transcriptional regulations and, more broadly, the functional consequences of processes out of the equilibrium in biology.

We revisit the problem of an elastic line (such as a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension $d=1+1$. Upon applying a transverse field, a delocalization transition is expected, beyond which the line is tilted macroscopically. We investigate this transition in the fixed tilt angle ensemble and within a “one-way” model where backward jumps are neglected. From recent results about directed polymers in the mathematics literature, and their connections to random matrix theory, we find that for a single line and a single strong defect this transition in the presence of point disorder coincides with the Baik–Ben Arous–Péché (BBP) transition for the appearance of outliers in the spectrum of a perturbed random matrix in the Gaussian unitary ensemble. This transition is conveniently described in the polymer picture by a variational calculation. In the delocalized phase, the ground state energy exhibits Tracy-Widom fluctuations. In the localized phase we show, using the variational calculation, that the fluctuations of the occupation length along the columnar defect are described by $f_{\mathrm{KPZ}}$, a distribution which appears ubiquitously in the Kardar-Parisi-Zhang universality class. We then consider a smooth density of columnar defect energies. Depending on how this density vanishes at its lower edge we find either (i) a delocalized phase only or (ii) a localized phase with a delocalization transition. We analyze this transition which is an infinite-rank extension of the BBP transition. The fluctuations of the ground state energy of a single elastic line in the localized phase (for fixed columnar defect energies) are described by a Fredholm determinant based on a new kernel, closely related to the kernel describing the largest real eigenvalues of the real Ginibre ensemble. The case of many columns and many nonintersecting lines, relevant for the study of the Bose glass phase, is also analyzed. The ground state energy is obtained using free probability and the Burgers equation. Connections with recent results on the generalized Rosenzweig-Porter model suggest that the localization of many polymers occurs gradually upon increasing their lengths.

The one-dimensional $\delta$-function interacting Bose gas (the Lieb-Liniger model) is an integrable system, which can model experiments with ultra-cold atoms in one-dimensional traps. Even though the model is integrable, integrability breaking effects are always present in the real-world experiments. In this work we consider the integrability breaking due to atomic loss, which is the most relevant effect in the experiments. We set up a framework for the exact computation of the losses of the canonical charges of the model, and compute an exact result for the energy loss due to the local $K$-body processes, valid for arbitrary $K$. Our result takes the form of multiple integrals, which are explicitly factorized in the experimentally relevant cases of $K=1,2,3$.

We show that there is genuine chaos in quantum dynamics by introducing a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for example, the Fubini-Study distance, the physical distance between two mutually orthogonal quantum states, can be very small. As a result, two quantum states, which are initially very close by physical distance, can diverge from each other during the ensuing quantum dynamical evolution. We are able to use physical distance to define the quantum Lyapunov exponent and the quantum chaos measure. The latter leads to a quantum analog of the classical Poincaré section, which maps out the regions where quantum dynamics is regular and the regions where it is chaotic. Three different systems—a kicked rotor, the three-site Bose-Hubbard model, and the spin-1/2 $XXZ$ model—are used to illustrate our results.

Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated with paths of different lengths is still missing. Here, we derive exact expressions for random-walk connectivity probabilities across any range of numbers of steps in a generic temporal, directed, and weighted network. This allows characterizing explicit connectivity realized by causal paths as well as implicit connectivity related to motifs of three nodes and two links called here pitchforks. We directly link such probabilities to the processes of tagging and sampling any quantity exchanged across the network, hence providing a natural framework to assess transport dynamics. Finally, we apply our theoretical framework to study ocean transport features in the Mediterranean Sea. We find that relevant transport structures, such as fluid barriers and corridors, can generate contrasting and counterintuitive connectivity patterns bringing novel insights into how ocean currents drive seascape connectivity.