We consider a rudimentary model for a heat engine, known as the Brownian gyrator, that consists of an overdamped system with two degrees of freedom in an anisotropic temperature field. Whereas the hallmark of the gyrator is a nonequilibrium steady-state curl-carrying probability current that can generate torque, we explore the coupling of this natural gyrating motion with a periodic actuation potential for the purpose of extracting work. We show that path lengths traversed in the manifold of thermodynamic states, measured in a suitable Riemannian metric, represent dissipative losses, while area integrals of a work density quantify work being extracted. Thus, the maximal amount of work that can be extracted relates to an isoperimetric problem, trading off area against length of an encircling path. We derive an isoperimetric inequality that provides a universal bound on the efficiency of all cyclic operating protocols, and a bound on how fast a closed path can be traversed before it becomes impossible to extract positive work. The analysis presented provides guiding principles for building autonomous engines that extract work from anisotropic fluctuations.

We investigate the spatial and temporal memory effects of traffic density and velocity in the Nagel-Schreckenberg cellular automaton model. We show that the two-point correlation function of vehicle occupancy provides access to spatial memory effects, such as headway, and the velocity autocovariance function to temporal memory effects such as traffic relaxation time and traffic compressibility. We develop stochasticity–density plots that permit determination of traffic density and stochasticity from the isotherms of first- and second-order velocity statistics of a randomly selected vehicle. Specifically, provided ergodicity and stationarity, these stochasticity–density plots permit a direct determination of traffic properties from crowdsourced measurements of velocities of vehicles. We illustrate the predictive prowess of the approach for crowdsourced vehicle speed data collected by anonymous smartphone measurements for the state of Massachusetts, USA, as a powerful alternative to classical traffic property estimates from spatially distributed user counts.

We study two interacting identical run-and-tumble particles (RTPs) in one dimension. Each particle is driven by a telegraphic noise and, in some cases, also subjected to a thermal white noise with a corresponding diffusion constant $D$. We are interested in the stationary bound state formed by the two RTPs in the presence of a mutual attractive interaction. The distribution of the relative coordinate $y$ indeed reaches a steady state that we characterize in terms of the solution of a second-order differential equation. We obtain the explicit formula for the stationary probability $P\left(y\right)$ of $y$ for two examples of interaction potential $V\left(y\right)$. The first one corresponds to $V\left(y\right)\sim \left|y\right|$. In this case, for $D=0$ we find that $P\left(y\right)$ contains a $\delta$ function part at $y=0$, signaling a strong clustering effect, together with a smooth exponential component. For $D>0$, the $\delta$ function part broadens, leading instead to weak clustering. The second example is the harmonic attraction $V\left(y\right)\sim y^2$ in which case, for $D=0$, $P\left(y\right)$ is supported on a finite interval. We unveil an interesting relation between this two-RTP model with harmonic attraction and a three-state single-RTP model in one dimension, as well as with a four-state single-RTP model in two dimensions. We also provide a general discussion of the stationary bound state, including examples where it is not unique, e.g., when the particles cannot cross due to an additional short-range repulsion.

We consider diffusion of particles on a lattice in the so-called dynamical mean-field regime (memory effects are neglected). Interactions are local, that is, only among particles at the same lattice site. It is shown that a statistical mechanics analysis that combines detailed balance and Widom's insertion formula allows for the derivation of an expression for transition rates in terms of the excess chemical potential. The rates reproduce the known dependence of self-diffusivity as the inverse of the thermodynamic factor. Soft-core interactions and general forms of the excess chemical potential (linear, quadratic, and cubic with the density) are considered.

The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g., within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrödinger equation and systematically derive a normal form for the emergence of radially symmetric blowup solutions from stationary ones. While this is an extensively studied problem, such a normal form, based on the methodology of asymptotics beyond all algebraic orders, applies to both the dimension-dependent and power-law-dependent bifurcations previously studied. It yields excellent agreement with numerics in both leading and higher-order effects, it is applicable to both infinite and finite domains, and it is valid in both critical and supercritical regimes.

We investigate the local (or occupation) time of a discrete-time random walk on a generic graph, and present a general method for calculating sample-path averages of local time functionals in terms of the resolvent of the transition matrix.

Cell membranes are heterogeneous with a variety of lipids, cholesterol, and proteins and are composed of domains of different compositions. Such heterogeneous environments make the transport of cholesterol complicated: cholesterol not only diffuses within a particular domain but also travels between domains. Cholesterol also flip-flops between upper and lower leaflets such that cholesterol may reside both within leaflets and in the central region between two leaflets. How the presence of multiple domains and the interdomain exchange of cholesterol would affect the cholesterol transport, however, remains elusive. In this study, therefore, we perform molecular dynamics simulations up to $100\mu \text{s}$ for ternary component lipid membranes, which consist of saturated lipids (dipalmitoylphosphatidylcholine, DPPC), unsaturated lipids (dilinoleylphosphatidylcholine, DIPC), and cholesterol. The ternary component membranes in our simulations form two domains readily: DPPC and DIPC domains. We find that the diffusion of cholesterol molecules is much more heterogeneous and non-Gaussian than expected for binary component lipid membranes of lipids and cholesterol. The non-Gaussian parameter of the cholesterol molecules is about four times larger in the ternary component lipid membranes than in the binary component lipid membranes. Such non-Gaussian and heterogeneous transport of cholesterol arises from the interplay among the interdomain kinetics, the different diffusivity of cholesterol in different domains, and the flip-flop of cholesterol. This suggests that in cell membranes that consist of various domains and proteins, the cholesterol transport can be very heterogeneous. We also find that the mechanism of the interdomain exchange differs for different domains: cholesterol tends to exit the DIPC domain along the central region of the membrane for the DIPC-to-DPPC transition, while the cholesterol is likely to exit the DPPC domain within the membrane leaflet for the DPPC-to-DIPC transition. Also, the interdomain exchange kinetics of cholesterol for the DPPC-to-DIPC transition is up to 7.9 times slower than the DIPC-to-DPPC transition.

The recent measurement of a very low dielectric constant, $\epsilon$, of water confined in nanometric slit pores leads us to reconsider the physical basis of ion partitioning into nanopores. For confined ions in chemical equilibrium with a bulk of dielectric constant ${\epsilon }_b>\epsilon$, three physical mechanisms, at the origin of ion exclusion in nanopores, are expected to be modified due to this dielectric mismatch: dielectric exclusion at the water-pore interface (with membrane dielectric constant, ${\epsilon }_m<\epsilon$), the solvation energy related to the difference in Debye-Hückel screening parameters in the pore, $\kappa$, and in the bulk ${\kappa }_b$, and the classical Born solvation self-energy proportional to ${\epsilon }^{-1}-{\epsilon }_b^{-1}$. Our goal is to clarify the interplay between these three mechanisms and investigate the role played by the Born contribution in ionic liquid-vapor (LV) phase separation in confined geometries. We first compute analytically the potential of mean force (PMF) of an ion of radius $R_i$ located at the center of a nanometric spherical pore of radius $R$. Computing the variational grand potential for a solution of confined ions, we then deduce the partition coefficients of ions in the pore versus $R$ and the bulk electrolyte concentration ${\rho }_b$. We show how the ionic LV transition, directly induced by the abrupt change of the dielectric contribution of the PMF with $\kappa$, is favored by the Born self-energy and explore the decrease of the concentration in the pore with $\epsilon$ both in the vapor and liquid states. Phase diagrams are established for various parameter values and we show that a signature of this phase transition can be detected by monitoring the total osmotic pressure as a function of $R$. For charged nanopores, these exclusion effects compete with the electrostatic attraction that imposes the entry of counterions into the pore to enforce electroneutrality. This study will therefore help in deciphering the respective roles of the Born self-energy and dielectric mismatch in experiments and simulations of ionic transport through nanopores.

Self-assembled granular materials can be utilized in many applications such as shock absorption and energy harvesting. Such materials are inherently discrete with an easy path to tunability through external applied forces such as stress or by adding more elements to the system. However, the self-assembly process is statistical in nature with no guarantee for repeatability, stability, or order of emergent final assemblies. Here we study both numerically and experimentally the two-dimensional self-assembly of free-floating disks with repulsive magnetic potentials confined to a boundary with embedded permanent magnets. Six different types of disks and seven boundary shapes are considered. An agent-based model is developed to predict the self-assembled patterns for any given disk type, boundary, and number of disks. The validity of the model is experimentally verified. While the model converges to a physical solution, these solutions are not always unique and depend on the initial position of the disks. The emerging patterns are classified into monostable patterns (i.e., stable patterns that emerge regardless of the initial conditions) and multistable patterns. We also characterize the emergent order and crystallinity of the emerging patterns. The developed model along with the self-assembly nature of the system can be key in creating re-programmable materials with exceptional nonlinear properties.

The notion of an evolutional deep neural network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only and are subsequently updated dynamically, without any further training, to provide an accurate prediction of the evolution of the PDE system. In this framework, the network parameters are treated as functions with respect to the appropriate coordinate and are numerically updated using the governing equations. By marching the neural network weights in the parameter space, EDNN can predict state-space trajectories that are indefinitely long, which is difficult for other neural network approaches. Boundary conditions of the PDEs are treated as hard constraints, are embedded into the neural network, and are therefore exactly satisfied throughout the entire solution trajectory. Several applications including the heat equation, the advection equation, the Burgers equation, the Kuramoto Sivashinsky equation, and the Navier-Stokes equations are solved to demonstrate the versatility and accuracy of EDNN. The application of EDNN to the incompressible Navier-Stokes equations embeds the divergence-free constraint into the network design so that the projection of the momentum equation to solenoidal space is implicitly achieved. The numerical results verify the accuracy of EDNN solutions relative to analytical and benchmark numerical solutions, both for the transient dynamics and statistics of the system.

The interaction between atomic Bose-Einstein condensate (BEC) and light field in an optical ring cavity gives rise to many interesting phenomena such as supersolid and movable self-trapped matter wave packets. Here we examined the collision of two self-trapped atomic matter wave packets in an optical ring cavity, and abundant colliding phenomena have been found in the system. Depending on the magnitude of colliding velocity, the collision dynamics exhibit very different features compared with the cavity-free case. When the initial colliding velocities of the two wave packets are small, they correlatedly oscillate around their initial equilibrium positions with a small amplitude. Increasing the collision velocity leads to severe scattering of the BEC atoms; after the collision, the two self-trapped wave packets usually break into small pieces. Interestingly, we found that such a medium velocity collision is of great phase sensitivity, which may make the system useful in precision matter wave interferometry. When the colliding velocity is further increased, in the bad cavity limit, the two wave packets collide phenomenally similar to two classical particles—they first approach each other, then separate with their shape virtually maintained. However, beyond the bad cavity limit, they experience severe spatial spreading.

Tipping elements in the Earth system have received increased scientific attention over recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are subdominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks of different size and with different coupling parameters.

Zygosity of diploid genome (i.e., degree to which two parental alleles of a gene have varied genetic sequences) adds another dimension to stochastic gene expression. The allelic imbalance in chromatin accessibility or divergence in regulatory sequences leads to fitness effects but the quantitative aspects thereof are largely left unexplored. We investigate diploid gene expression systems with homozygous (the same) and heterozygous (varied) combination of alleles in cis-regulatory sequences, not in structural gene loci, and characterize the zygosity-associated stochastic fluctuations in protein abundance. An emerging feat of heterozygosity is its counterintuitive capacity for genetic noise control. Especially when the noise is dominantly contributed to by the fluctuations in duty cycle (“reliability”) rather than in process speed (“productivity”) of gene expression machinery, its interallelic discrepancy acts to reduce the gene expression noise. These findings offer a novel insight into the rich repertoire of balancing selection enriched in the regulatory elements of immune response genes.

This study reports the development of a three-dimensional numerical model for acoustic interactions with a microscale sessile droplet under surface acoustic wave (SAW) excitation using the lattice Boltzmann method (LBM). We first validate the model before SAW interactions are added. The results demonstrate good agreement with the analytical results for thermodynamic consistency, Laplace law, static contact angle on a flat surface, and droplet oscillation. We then investigate SAW interactions on the droplet, with resonant frequencies ranging 61.7–250.1 MHz. According to our findings, an increase in wave amplitude elicits an increase in streaming velocity inside the droplet, causing internal mixing, and further increase in wave amplitude leads to pumping and jetting. The boundaries of wave amplitude at various resonant frequencies are predicted for mixing, pumping, and jetting modes. The modeling predictions on the roles of forces (SAW, interfacial tension, inertia, and viscosity) on the dynamics of mixing, pumping, and jetting of a droplet are in good agreement with observations and experimental data. The model is further applied to investigate the effects of SAW substrate surface wettability, viscosity ratio, and interfacial tension on SAW actuation onto the droplet. This work demonstrates the capability of the LBM in the investigation of acoustic wave interactions between SAW and a liquid medium.

Particle or energy transfer through quantum networks is determined by network topology and couplings to environments. This study examines the combined effect of topology and external couplings on the efficiency of directional quantum transfer through quantum networks. We consider a microscopic model of qubit networks coupled to external vibrations by Holstein and Peierls couplings. By treating the positions of the network sites and the site-dependent phonon frequencies as independent variables, we determine the Hamiltonian parameters corresponding to minimum transfer time by Bayesian optimization. The results show that Holstein couplings may accelerate transfer through suboptimal network configurations but cannot accelerate quantum dynamics beyond the limit of the transfer time in an optimal phonon-free configuration. By contrast, Peierls couplings distort the optimal networks to accelerate quantum transfer through configurations with less than six sites. However, the speed-up offered by Peierls couplings decreases with the network size and disappears for networks with more than seven sites. For networks with seven sites or more, Peierls couplings distort the optimal network configurations and change the mechanism of quantum transfer but do not affect the lower limit of the transfer time. The machine-learning approach demonstrated here can be applied to determine quantum speed limits in other applications.

Sine-square deformation (SSD) is a treatment proposed in quantum systems, which spatially modifies a Hamiltonian, gradually decreasing the local energy scale from the center of the system toward the edges by a sine-squared envelope function. It is known to serve as a good boundary condition as well as to provide physical quantities reproducing those of the infinite-size systems. We apply the SSD to one- and two-dimensional classical Ising models. Based on the analytical calculations and Monte Carlo simulations, we find that the classical SSD system is regarded as an extended canonical ensemble of a local subsystem, each characterized by its own effective temperature. This effective temperature is defined by normalizing the system temperature by the deformed local energy scale. A single calculation for a given system temperature provides a set of physical quantities of various temperatures that quantitatively reproduces well those of the uniform system.

Work extraction protocol is always a significant issue in the context of quantum batteries, in which the notion of ergotropy is used to quantify a particular amount of energy that can be extracted through unitary processes. Given the total amount of energy stored in a quantum system, quantifying wasted energy after the ergotropy extraction is a question to be considered when undesired coupling with thermal reservoirs is taken into account. In this paper, we show that some amount of energy can be lost when we extract ergotropy from a quantum system and quantified by the exergy of passive states. Through a particular example, one shows that ergotropy extraction can be done by preserving the quantum correlations of a quantum system. Our study opens the perspective for new advances in open system quantum batteries able to explore exergy stored as quantum correlations.

Measures are proposed for reliably estimating the entropy of bits produced in an entropy source using a chaotic physical system. The measures are reliable with respect to a “guessing” attack and depend on the end-to-end method of transfer of entropy from the chaotic physical system to the bit entropy source. Fixed partitions are considered to correspond with practical methods for fast digital sampling of analog signals. We propose two different measures corresponding to the batch and streaming modes of entropy transfer. Numerical examples are provided to demonstrate features of dependence of the batch and stream entropy on fixed partitions with uniform or nonuniform types of chaos.