We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic dissipation, and the analysis of thermodynamic consistency of the currents in the light of symmetries. Employing the large deviation techniques presented by Gingrich et al. [Phys. Rev. Lett. 116, 120601 (2016)] and Pietzonka, Barato, and Seifert [Phys. Rev. E 93, 052145 (2016)], we provide a short proof of the loose uncertainty principle, and prove a tighter uncertainty relation for a class of thermodynamically consistent currents $J$. Our bound involves a measure of partial entropy production, that we interpret as the least amount of entropy that a system sustaining current $J$ can possibly produce, at a given steady state. We provide a complete mathematical discussion of quadratic bounds which allows one to determine which are optimal, and finally we argue that the relationship for the Fano factor of the entropy production rate $\mathrm{var}\sigma /\mathrm{mean}\sigma \ge 2$ is the most significant realization of the loose bound. We base our analysis both on the formalism of diffusions, and of Markov jump processes in the light of Schnakenberg's cycle analysis.

Fractional Brownian motion is a self-affine, non-Markovian, and translationally invariant generalization of Brownian motion, depending on the Hurst exponent $H$. Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time $t_{+}$ the process is positive, the maximum $m$ it achieves, and the time $t_{\max }$ when this maximum is taken. Using a perturbative expansion around Brownian motion ($H=\frac{1}{2}$), we give the first-order result for the probability distribution of these three variables and the joint distribution of $m$ and $t_{\max }$. Our analytical results are tested and found to be in excellent agreement, with extensive numerical simulations for both $H>\frac{1}{2}$ and $H<\frac{1}{2}$. This precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.

We study a simple model for social learning agents in a restless multiarmed bandit. There are $N$ agents, and the bandit has $M$ good arms that change to bad with the probability $q_c/N$. If the agents do not know a good arm, they look for it by a random search (with the success probability $q_I$) or copy the information of other agents' good arms (with the success probability $q_O$) with probabilities $1-p$ or $p$, respectively. The distribution of the agents in $M$ good arms obeys the Yule distribution with the power-law exponent $1+\gamma$ in the limit $N,M\to \infty ,$ and $\gamma =1+\frac{(1-p)q_I}{p{q}_O}$. The system shows a phase transition at $p_c=\frac{q_I}{q_I+q_o}$. For $p<p_c(>p_c)$, the variance of $N_1$ per agent is finite (diverges as $\propto N^{2-\gamma }$ with $N$). There is a threshold value $N_s$ for the system size that scales as $ln{N}_s\propto 1/(\gamma -1)$. The expected value of the number of the agents with a good arm $N_1$ increases with $p$ for $N>N_s$. For $p>p_c$ and $N<N_s$, all agents tend to share only one good arm. If the shared arm changes to be bad, it takes a long time for the agents to find another good one. $\text{E}\left(N_1\right)$ decreases to zero as $p\to 1$, which is referred to as the “echo chamber.”

Extended Vicsek fractals (EVF) are the structures constructed by introducing linear spacers into traditional Vicsek fractals. Here we study the Laplacian spectra of the EVF. In particularly, the recurrence relations for the Laplacian spectra allow us to obtain an analytic expression for the sum of all inverse nonvanishing Laplacian eigenvalues. This quantity characterizes the large-scale properties, such as the gyration radius of the polymeric structures, or the global mean-first passage time for the random walk processes. Introduction of the linear spacers leads to local heterogeneities, which reveal themselves, for example, in the dynamics of EVF under external forces.

We contrast the dynamics in model unentangled polymer melts of chains of three different stiffnesses: flexible, intermediate, and rodlike. Flexible and rodlike chains, which readily solidify into close-packed crystals (respectively, with randomly oriented and nematically aligned chains), display simple melt dynamics with Arrhenius temperature dependence and a discontinuous change upon solidification. Intermediate-stiffness chains, however, are fragile glass-formers displaying Vogel-Fulcher dynamical arrest, despite the fact that they also possess a nematic-close-packed crystalline ground state. To connect this difference in dynamics to the differing microstructure of the melts, we examine how various measures of structure, including cluster-level metrics recently introduced in studies of colloidal systems, vary with chain stiffness and temperature. No clear static-structural cause of the dynamical arrest is found. However, we find that the intermediate-stiffness chains display qualitatively different dynamical heterogeneity. Specifically, their stringlike motion (cooperative rearrangement) is correlated along chain backbones in a way not found for either flexible or rodlike chains. This activated “crawling” motion is clearly associated with the dynamical arrest observed in these systems, and illustrates one way in which factors controlling the crystallization versus glass formation competition in polymers can depend nonmonotonically on chain stiffness.

We propose a model molecule to investigate microscopic properties of a binary mixture with a closed-loop coexistence region. The molecule is comprised of a Lennard-Jones particle and a uniaxial quadrupole. Gibbs ensemble Monte Carlo simulations demonstrate that the high-density binary fluid of the molecules with the quadrupoles of the same magnitude but of the opposite signs can show closed-loop immiscibility. We find that an increase in the magnitude of the quadrupoles causes a shrinkage of the coexistence region. Molecular dynamics simulations also reveal that aggregates with two types of molecules arranged alternatively are formed in the stable one-phase region both above and below the coexistence region. String structures are dominant below the lower critical solution temperature, while branched aggregates are observed above the upper critical solution temperature. We conclude that the anisotropic interaction between the quadrupoles of the opposite signs plays a crucial role in controlling these properties of the phase behavior.

Markov state modeling (MSM) has recently emerged as one of the key techniques for the discovery of collective variables and the analysis of rare events in molecular simulations. In particular in biochemistry this approach is successfully exploited to find the metastable states of complex systems and their evolution in thermal equilibrium, including rare events, such as a protein undergoing folding. The physics of sliding friction and its atomistic simulations under external forces constitute a nonequilibrium field where relevant variables are in principle unknown and where a proper theory describing violent and rare events such as stick slip is still lacking. Here we show that MSM can be extended to the study of nonequilibrium phenomena and in particular friction. The approach is benchmarked on the Frenkel-Kontorova model, used here as a test system whose properties are well established. We demonstrate that the method allows the least prejudiced identification of a minimal basis of natural microscopic variables necessary for the description of the forced dynamics of sliding, through their probabilistic evolution. The steps necessary for the application to realistic frictional systems are highlighted.

We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.

We use space-charge (SC) theory (also called the capillary pore model) to describe the ionic conductance, $G$, of charged carbon nanotubes (CNTs). Based on the reversible adsorption of hydroxyl ions to CNT pore walls, we use a Langmuir isotherm for surface ionization and make calculations as a function of pore size, salt concentration $c$, and $p\mathrm{H}$. Using realistic values for surface site density and $p\mathrm{K}$, SC theory well describes published experimental data on the conductance of CNTs. At extremely low salt concentration, when the electric potential becomes uniform across the pore, and surface ionization is low, we derive the scaling $G\propto \sqrt{c}$, while for realistic salt concentrations, SC theory does not lead to a simple power law for $G\left(c\right)$.

Photosynthesis has been a long-standing research interest due to its fundamental importance. Recently, studies on photosynthesis processes also have inspired attention from a thermodynamical aspect when considering photosynthetic apparatuses as biological quantum heat engines. Quantum coherence is shown to play a crucial role in enhancing the performance of these quantum heat engines. Based on the experimentally reported structure, we propose a quantum heat engine model with a non-Markovian vibrational mode. We show that one can obtain a performance enhancement easily for a wide range of parameters in the presence of the vibrational mode. Our results provide insights into the photosynthetic processes and a design principle mimicking natural organisms.

We investigate the two-dimensional $q=3$ and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number $z$ of equivalent neighbors. For not-too-large $z$, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges, the transitions become discontinuous. For $q=3$ we locate a tricritical point separating the continuous and discontinuous transitions near $z=80$, and a critical fixed point between $z=8$ and 12. For $q=4$ the transition becomes discontinuous for $z>16$. The scaling behavior of the $q=4$ model with $z=16$ approximates that of the $q=4$ merged critical-tricritical fixed point predicted by the renormalization scenario.

Information flow or information transfer the widely applicable general physics notion can be rigorously derived from first principles, rather than axiomatically proposed as an ansatz. Its logical association with causality is firmly rooted in the dynamical system that lies beneath. The principle of nil causality that reads, an event is not causal to another if the evolution of the latter is independent of the former, which transfer entropy analysis and Granger causality test fail to verify in many situations, turns out to be a proven theorem here. Established in this study are the information flows among the components of time-discrete mappings and time-continuous dynamical systems, both deterministic and stochastic. They have been obtained explicitly in closed form, and put to applications with the benchmark systems such as the Kaplan-Yorke map, Rössler system, baker transformation, Hénon map, and stochastic potential flow. Besides unraveling the causal relations as expected from the respective systems, some of the applications show that the information flow structure underlying a complex trajectory pattern could be tractable. For linear systems, the resulting remarkably concise formula asserts analytically that causation implies correlation, while correlation does not imply causation, providing a mathematical basis for the long-standing philosophical debate over causation versus correlation.

We study the effect of superdiffusion on the instability in reaction-diffusion systems. It is shown that reaction-superdiffusion systems close to a Turing instability are equivalent to a time-dependent Ginzburg-Landau model and the corresponding free energy is introduced. This generalized free energy which depends on the superdiffusion exponent governs the stability, dynamics, and the fluctuations of reaction-superdiffusion systems near the Turing bifurcation. In addition, we show that for a general $n$-component reaction-superdiffusion system, a fractional complex Ginzburg-Landau equation emerges as the amplitude equation near a Hopf instability. Numerical simulations of this equation are carried out to illustrate the effect of superdiffusion on spatiotemporal patterns. Finally, the effect of superdiffusion on the instability in the Brusselator model, as a special case of reaction-diffusion systems, is studied. In general, superdiffusion introduces a new parameter that changes the behavior of the system near the instability.

Efficient uptake of prey and nutrients from the environment is an important component in the fitness of all microorganisms, and its dependence on size may reveal clues to the origins of evolutionary transitions to multicellularity. Because potential benefits in uptake rates must be viewed in the context of other costs and benefits of size, such as varying predation rates and the increased metabolic costs associated with larger and more complex body plans, the uptake rate itself is not necessarily that which is optimized by evolution. Uptake rates can be strongly dependent on local organism geometry and its swimming speed, providing selective pressure for particular arrangements. Here we examine these issues for choanoflagellates, filter-feeding microorganisms that are the closest relatives of the animals. We explore the different morphological variations of the choanoflagellate Salpingoeca rosetta, which can exist as a swimming cell, as a sessile thecate cell, and as colonies of cells in various shapes. In the absence of other requirements and in a homogeneously nutritious environment, we find that the optimal strategy to maximize filter-feeding by the collar of microvilli is to swim fast, which favors swimming unicells. In large external flows, the sessile thecate cell becomes advantageous. Effects of prey diffusion are discussed and also found to be to the advantage of the swimming unicell.

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, $R_a$, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of $R_a$ is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as $R_a$ increases. Critical values of $R_a$ are identified for the construction of a nonslip base at various angles of inclination.

The paper shows that it is possible to combine the free-energy lattice Boltzmann approach to multiphase modeling of fluids involving both liquid and vapor with the partial bounce back lattice Boltzmann approach to modeling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce-back approach, an effective media parameter or bounce-back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (gray nodes), and solids (black nodes). The use of the wetting potential combined with the bounce-back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid in material systems. Results for phase separation, permeability, contact angle, and wicking in gray media are shown. Sorption is explored in small sections of model multiscale porous systems to demonstrate two-step desorption, sorption hysteresis, and the ink-bottle effect.

Gelation transitions in a colloidal system, where there is a strong reversible attraction between small, soft microgels and large, hard spheres, are systematically investigated. Different from widely studied depletion attraction systems that are also two-component systems, the strong attraction between small solvent and large solute particles introduces bridging attractions between large solute particles. We conclusively demonstrate that the formation of physical gels at the intermediate volume fraction of our bridging attraction system follows more closely with the percolation line that is in stark contrast to what is observed in depletion attraction systems, where the gelation transition is related with the frustrated spinodal separation, not a purely kinetic phenomenon. Our results introduce a different way to control gelation transitions in spherical colloidal systems, and imply that people need to be prudent when generalizing the physical picture of the gelation transitions obtained from systems with different origins of effective attraction as the solvent molecule may play important roles.