We report a systematic study of the forward and reverse transition probability density functions (TPDFs) and entropy production in a nonequilibrium steady state (NESS). The NESS is realized in a two-layer colloidal system, in which the bottom-layer colloidal crystal provides a two-dimensional periodic potential $U_0(x,y)$ for the top-layer diffusing particles. By tilting the sample at an angle with respect to gravity, a tangential component of the gravitational force $F$ is applied to the diffusing particles, which breaks the detailed balance (DB) condition and generates a steady particle flux along the [1,0] crystalline orientation. While both the measured forward and reverse TPDFs reveal interesting space-time dependence, their ratio is found to be independent of time and obeys a DB-like relation. The experimental results are in good agreement with the theoretical predictions. This study thus provides a better understanding on how entropy is generated and heat is dissipated to the reservoir during a NESS transition process. It also demonstrates the applications of the two-layer colloidal system in the study of NESS transition dynamics.

Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more proactive decision making, in which environmental information is sensed and exploited more actively and effectively. Understanding the fundamental relation between fitness and information is therefore crucial to clarify the limits and universal properties of adaptation. In this work, we elucidate the underlying stochastic and information-thermodynamic structure in this process, by deriving causal fluctuation relations (FRs) of fitness and information. Combined with a duality between phenotypic and environmental dynamics, the FRs reveal the limit of fitness gain, the relation of time reversibility with the achievability of the limit, and the possibility and condition for gaining excess fitness due to environmental fluctuation. The loss of fitness due to causal constraints and the limited capacity of real organisms is shown to be the difference between time-forward and time-backward path probabilities of phenotypic and environmental dynamics. Furthermore, the FRs generalize the concept of the evolutionary stable state (ESS) for fluctuating environment by giving the probability that the optimal strategy on average can be invaded by a suboptimal one owing to rare environmental fluctuation. These results clarify the information-thermodynamic structures in adaptation and evolution.

By means of extensive coupled molecular dynamics–lattice Boltzmann simulations, accounting for grain dynamics and subparticle resolution of the fluid phase, we analyze steady inertial granular flows sheared by a viscous fluid. We show that, for a broad range of system parameters (shear rate, confining stress, fluid viscosity, and relative fluid-grain density), the frictional strength and packing fraction can be described by a modified inertial number incorporating the fluid effect. In a dual viscous description, the effective viscosity diverges as the inverse square of the difference between the packing fraction and its jamming value, as observed in experiments. We also find that the fabric and force anisotropies extracted from the contact network are well described by the modified inertial number, thus providing clear evidence for the role of these key structural parameters in dense suspensions.

The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner et al., J. Bacteriol. 182, 2793 (2000)]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982)]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.

A two-step contagion model with a single seed serves as a cornerstone for understanding the critical behaviors and underlying mechanism of discontinuous percolation transitions induced by cascade dynamics. When the contagion spreads from a single seed, a cluster of infected and recovered nodes grows without any cluster merging process. However, when the contagion starts from multiple seeds of $O\left(N\right)$ where $N$ is the system size, a node weakened by a seed can be infected more easily when it is in contact with another node infected by a different pathogen seed. This contagion process can be viewed as a cluster merging process in a percolation model. Here we show analytically and numerically that when the density of infectious seeds is relatively small but $O\left(1\right)$, the epidemic transition is hybrid, exhibiting both continuous and discontinuous behavior, whereas when it is sufficiently large and reaches a critical point, the transition becomes continuous. We determine the full set of critical exponents describing the hybrid and the continuous transitions. Their critical behaviors differ from those in the single-seed case.

We study the behavior of a waterlike liquid inside the gate of a biological ion channel following the basic geometry of the well studied potassium channel KcsA. We calculate the three-dimensional density distribution $\rho \left(\mathbf{r}\right)$ of the liquid within the framework of classical density functional theory and observe the formation of a low density region (bubble) when the gate is narrow. This observation corresponds to a finite-size form of capillary evaporation and supports the so-called bubble-gate theory. From the density profile we also compute the energy landscape of the gate and the energy required to change the gate from a closed (narrow) to an open (wide) state and vice versa.

We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction $\varphi$, inelasticity of collisions as measured by a parameter $Q$, and applied uniform shear strain rate $\dot{\gamma }$. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no interparticle Coulombic friction. Mapping the phase diagram in the $(\varphi ,Q)$ plane for small $\dot{\gamma }$, we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small $Q$ (strongly inelastic collisions). At small $Q$, we show that, upon increasing $\dot{\gamma }$, the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the $(\varphi ,\dot{\gamma })$ plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing $\dot{\gamma }$ at fixed $\varphi$, we find that discontinuous shear thickening can result if $\dot{\gamma }$ is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of $\dot{\gamma }$.

The local time of a stochastic process quantifies the amount of time that sample trajectories $x\left(\tau \right)$ spend in the vicinity of an arbitrary point $x$. For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on the local times of Lévy random walks (Lévy flights), which correspond to fractional diffusion equations.

The ability of a honeybee swarm to select the best nest site plays a fundamental role in determining the future colony's fitness. To date, the nest-site selection process has mostly been modeled and theoretically analyzed for the case of binary decisions. However, when the number of alternative nests is larger than two, the decision-process dynamics qualitatively change. In this work, we extend previous analyses of a value-sensitive decision-making mechanism to a decision process among $N$ nests. First, we present the decision-making dynamics in the symmetric case of $N$ equal-quality nests. Then, we generalize our findings to a best-of-$N$ decision scenario with one superior nest and $N-1$ inferior nests, previously studied empirically in bees and ants. Whereas previous binary models highlighted the crucial role of inhibitory stop-signaling, the key parameter in our new analysis is the relative time invested by swarm members in individual discovery and in signaling behaviors. Our new analysis reveals conflicting pressures on this ratio in symmetric and best-of-$N$ decisions, which could be solved through a time-dependent signaling strategy. Additionally, our analysis suggests how ecological factors determining the density of suitable nest sites may have led to selective pressures for an optimal stable signaling ratio.

Inspired by dynamic similarity in fluid systems, we have derived a general dimensionless form for locomotion in granular materials, which is validated in experiments and discrete element method (DEM) simulations. The form instructs how to scale size, mass, and driving parameters in order to relate dynamic behaviors of different locomotors in the same granular media. The scaling can be derived by assuming intrusion forces arise from resistive force theory or equivalently by assuming the granular material behaves as a continuum obeying a frictional yield criterion. The scalings are experimentally confirmed using pairs of wheels of various shapes and sizes under many driving conditions in a common sand bed. We discuss why the two models provide such a robust set of scaling laws even though they neglect a number of the complexities of granular rheology. Motivated by potential extraplanetary applications, the dimensionless form also implies a way to predict wheel performance in one ambient gravity based on tests in a different ambient gravity. We confirm this using DEM simulations, which show that scaling relations are satisfied over an array of driving modes even when gravity differs between scaled tests.

About three quarters of our DNA is wrapped into nucleosomes: DNA spools with a protein core. It is well known that the affinity of a given DNA stretch to be incorporated into a nucleosome depends on the geometry and elasticity of the basepair sequence involved, causing the positioning of nucleosomes. Here we show that DNA elasticity can have a much deeper effect on nucleosomes than just their positioning: it affects their “identities”. Employing a recently developed computational algorithm, the mutation Monte Carlo method, we design nucleosomes with surprising physical characteristics. Unlike any other nucleosomes studied so far, these nucleosomes are short-lived when put under mechanical tension whereas other physical properties are largely unaffected. This suggests that the nucleosome, the most abundant DNA-protein complex in our cells, might more properly be considered a class of complexes with a wide array of physical properties, and raises the possibility that evolution has shaped various nucleosome species according to their genomic context.

One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single-stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motor's fidelity does not depend on details of the motor-junction interaction, such as whether the interaction is passive or active. Analysis of the copying fidelity can still be used as a tool for investigating the junction kinetics.

We study decomposition of geometrically enforced nematic topological defects bearing relatively large defect strengths $m$ in effectively two-dimensional planar systems. Theoretically, defect cores are analyzed within the mesoscopic Landau–de Gennes approach in terms of the tensor nematic order parameter. We demonstrate a robust tendency of defect decomposition into elementary units where two qualitatively different scenarios imposing total defect strengths on a nematic region are employed. Some theoretical predictions are verified experimentally, where arrays of defects bearing charges $m=\pm 1$ and even $m=\pm 2$ are enforced within a plane-parallel nematic cell using an atomic force microscopy scribing method.

Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a nonvanishing spin current that is locally conserved except at the boundaries. We demonstrate that with suitably chosen boundary target states one can solve the many-body Lindblad equation exactly in any dimension. As solution we obtain pure states at any finite value of the dissipation strength and any system size. They are characterized by a helical stationary magnetization profile and a ballistic spin current which is independent of system size, even when the quantum spin system is not integrable. These results are derived in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its higher-spin generalizations, which include the integrable spin-1 Zamolodchikov-Fateev model and the biquadratic Heisenberg chain.

Plant leaf size varies by more than three orders of magnitude, from a few millimeters to over one meter. Conifer leaves, however, are relatively short and the majority of needles are no longer than 6 cm. The reason for the strong confinement of the trait-space is unknown. We show that sugars produced near the tip of long needles cannot be exported efficiently, because the pressure required to drive vascular flow would exceed the greatest available pressure (the osmotic pressure). This basic constraint leads to the formation of an inactive region of stagnant fluid near the needle tip, which does not contribute to sugar flow. Remarkably, we find that the size of the active part does not scale with needle length. We predict a single maximum needle size of 5 cm, in accord with data from 519 conifer species. This could help rationalize the recent observation that conifers have significantly smaller leaves than angiosperms, and provide a biophysical explanation for this intriguing difference between the two largest groups of plants.

Even after decades of research, the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time $\tau$, we obtain the statistics of first detection events for quantum dynamics on a lattice, with the detector located at the origin. A quantum renewal equation for a first detection wave function, in terms of which the first detection probability can be calculated, is derived. This formula gives the relation between first detection statistics and the solution of the corresponding Schrödinger equation in the absence of measurement. We illustrate our results with tight-binding quantum walk models. We examine a closed system, i.e., a ring, and reveal the intricate influence of the sampling time $\tau$ on the statistics of detection, discussing the quantum Zeno effect, half dark states, revivals, and optimal detection. The initial condition modifies the statistics of a quantum walk on a finite ring in surprising ways. In some cases, the average detection time is independent of the sampling time while in others the average exhibits multiple divergences as the sampling time is modified. For an unbounded one-dimensional quantum walk, the probability of first detection decays like ${\left(\text{time}\right)}^{(-3)}$ with superimposed oscillations, with exceptional behavior when the sampling period $\tau$ times the tunneling rate $\gamma$ is a multiple of $\pi /2$. The amplitude of the power-law decay is suppressed as $\tau \to 0$ due to the Zeno effect. Our work, an extended version of our previously published paper, predicts rich physical behaviors compared with classical Brownian motion, for which the first passage probability density decays monotonically like ${\left(\text{time}\right)}^{-3/2}$, as elucidated by Schrödinger in 1915.

We study the dynamic process occurring when a granular assembly is displaced by a solid impactor. The momentum transfer from the impactor to the target is shown to occur through sporadic, normal collisions of high force carrying grains at the intruder surface. We therefore describe the stopping force of the impact through a collisional-based model. To verify the model in impact experiments, we determine the forces acting on an intruder decelerating through a dense granular medium by using high-speed imaging of its trajectory. By varying the intruder shape and granular target, intruder-grain interactions are inferred from the consequent path. As a result, we connect the drag to the effect of intruder shape and grain density based on a proposed collisional model.

Stem cells are identical in many scales, they share the same molecular composition, DNA, genes, and genetic networks, yet they should acquire different properties to form a functional tissue. Therefore, they must interact and get some external information from their environment, either spatial (dynamical fields) or temporal (lineage). In this paper we test to what extent coupled chemical and physical fields can underlie the cell's positional information during development. We choose the root apical meristem of Arabidopsis thaliana to model the emergence of cellular patterns. We built a model to study the dynamics and interactions between the cell divisions, the local auxin concentration, and physical elastic fields. Our model recovers important aspects of the self-organized and resilient behavior of the observed cellular patterns in the Arabidopsis root, in particular, the reverse fountain pattern observed in the auxin transport, the PIN-FORMED (protein family of auxin transporters) polarization pattern and the accumulation of auxin near the region of maximum curvature in a bent root. Our model may be extended to predict altered cellular patterns that are expected under various applied auxin treatments or modified physical growth conditions.

Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.

We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, which undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat machine depends upon the interaction strength between the ions, the magnetic fields, and the measurement cost. In our model, the coupling to the hot and the cold baths is never switched off in an alternative fashion during the heat cycle, unlike other existing proposals of quantum heat engines. This makes our proposal experimentally realizable using current tapped-ion technology.