Bacterial cells use run-and-tumble motion to climb up attractant concentration gradient in their environment. By extending the uphill runs and shortening the downhill runs the cells migrate towards the higher attractant zones. Motivated by this, we formulate a reinforcement learning (RL) algorithm where an agent moves in one dimension in the presence of an attractant gradient. The agent can perform two actions: either persistent motion in the same direction or reversal of direction. We assign costs for these actions based on the recent history of the agent's trajectory. We ask the question: which RL strategy works best in different types of attractant environment. We quantify efficiency of the RL strategy by the ability of the agent (a) to localize in the favorable zones after large times, and (b) to learn about its complete environment. Depending on the attractant profile and the initial condition, we find an optimum balance is needed between exploration and exploitation to ensure the most efficient performance.

Metallic glasses have mechanical properties, which exhibit avalanches in the disguise of stress drops. We study these phenomena in a classical metallic glass system Cu-Zr-Al by athermal quasistatic shear and varying the element concentrations and for pure Cu-Zr 50/50 case the cooling rate. The resulting mechanical properties are close to the behavior found experimentally. At small strains, the pristine systems are akin to other glassy systems with a so-called gap distribution with a small positive exponent. Critical avalanching behavior is found only approaching the yield point. The post-yield stress drops are universal, and the gap distribution becomes flat.

Three types of cycles are identified in the quantum jump trajectories of the Scovil–Schulz-DuBois (SSDB) machine: An R cycle as refrigeration, an H cycle as a heat engine, and an N cycle in which the machine is neutral. The statistics of these cycles are investigated via a semi-Markov process method. We find that in the large time limit, whether the machine operates as a heat engine or refrigerator depends on the ratio between the numbers of R cycles and H cycles per unit time. Further increasing the hot bath temperature above a certain threshold does not increase the machine's power output. The cause is that, in this situation, the N cycle has a greater probability than the H cycle and R cycle. Although the SSDB machine operates by randomly switching between these three cycles, at the level of a single quantum jump trajectory, its heat engine efficiency and the refrigerator's coefficient of performance remain constant.

We study a Brownian motor that consists of two linearly coupled particles moving in a symmetric periodic potential and subjected to an unbiased harmonic driving in combination with a constant external force. Although a trajectory of the single-particle system must also be a valid trajectory of the corresponding coupled-particle system, the stability of the trajectory does not necessarily hold. It is revealed that, for proper strength of the interparticle coupling $K$, parametric resonance, which may break the stability of the trajectory, emerges. As a consequence, the system may fall into other attractors, regular or chaotic, and the mobility of the motor may be largely changed or even reversed. Absolute negative mobility in a much wider regime of parameter is then observed. Furthermore, the so induced absolute negative mobility is much more robust under the perturbation of external noise. This provides an effective way of tuning the collective mobility of a Brownian motor via adjusting its internal interactions only.

Thermodynamic uncertainty relation (TUR) bounds coherence in stochastic oscillatory systems. In this paper, we show that both dynamical and thermodynamic bounds play important roles for the excitable oscillators, e.g., neurons. Firstly, we investigate the trade-off between coherence and dissipation both in the sub- and superthreshold regions for a single excitable unit, where both the TUR and the saddle-node on an invariant circle (SNIC) bounds constrain the fluctuation of interspike intervals. Secondly, we show that the widely studied phenomenon called coherence resonance, where there exists a noise strength to make the oscillatory responses of the system most coherent, is also bounded by the TUR in the one-dimensional excitable phase model. Finally, we study the coherence-dissipation relation in ensembles of strongly coupled excitable oscillators.

We consider the problem of soliton mean-field interaction for the class of asymptotically integrable equations, where the notion of asymptotic integrability means that the Hamilton equations for a high-frequency wave packet's propagation along a large-scale background wave have an integral of motion. Using Stokes' remark, we transform this integral to an integral for the soliton equations of motion and then derive the Hamilton equations for the soliton dynamics in a universal form expressed in terms of the Riemann invariants for the hydrodynamic background wave. The physical properties are specified by the concrete expressions for the Riemann invariants. The theory is illustrated by its application to soliton dynamics, which is described by the Kaup-Boussinesq system.

We present a comprehensive theoretical analysis of thermo-optical multistability in two coupled silica microresonators with identical and slightly different partial eigenfrequencies. We consider a unidirectionally pumped system with a relatively low total $Q$-factor, where thermo-optical nonlinearity dominates. To analyze the system behavior, we employ a dynamical system approach that takes into account the hierarchy of the timescales associated with optical and thermal processes. We show that up to nine stationary states are possible for the same system parameters and that no more than four of them can be stable. Additionally, self-oscillation regimes are observed within specific parameter ranges. Bifurcations are discussed and nontrivial hysteretic switchings between light states under smooth pump frequency sweeping for different pump powers are demonstrated. It is also shown that even small intermode detuning can affect the dynamics of the system dramatically. This intriguing phenomenon is of fundamental interest and may potentially be used in the development of ultrasensitive sensors when operating near a bifurcation point, which is also discussed.

Energy considerations can significantly affect the behavior of a population of energy-consuming agents with limited energy budgets, for instance, in the movement process of people in a city. We consider a population of interacting agents with an initial energy budget walking on a graph according to an exploration and return (to home) strategy that is based on the current energy of the person. Each move reduces the available energy depending on the flow of movements and the strength of interactions, and the movement ends when an agent returns home with a negative energy. We observe that a uniform distribution of initial energy budgets results in a larger number of visited sites per consumed energy (efficiency) compared to case that all agents have the same initial energy if return to home is relevant from the beginning of the process. The uniform energy distribution also reduces the amount of uncertainties in the total travel times (entropy production) which is more pronounced when the strength of interactions and exploration play the relevant role in the movement process. That is, variability in the energies can help to increase the efficiency and reduce the entropy production especially in presence of strong interactions.

The timings of several cellular events like cell lysis, cell division, or pore formation in endosomes are regulated by the time taken for the relevant proteins to cross a threshold in number or concentration. Since protein synthesis is stochastic, the threshold crossing time is a first passage problem. The exact distributions of these first passage processes have been obtained recently for unregulated and autoregulated genes. Many proteins are however regulated by post-transcriptional regulation, controlled by small noncoding RNAs (sRNAs). Certain mathematical models of gene expression with post-transcriptional sRNA regulation have been recently exactly mapped to models without sRNA regulation. Utilizing this mapping and the exact distributions, we calculate exact results on fluctuations (full distribution, all cumulants, and characteristic times) of protein threshold crossing times in the presence of sRNA regulation. We derive two interesting predictions from these exact results. We show that the size of the fluctuation of the threshold crossing times have a nonmonotonic U-shaped behavior as a function of the rates of binding and unbinding of the sRNA-mRNA complex. Thus there are optimal parameters that minimize noise. Furthermore, the fluctuations in models with sRNA regulation may be higher or lower compared to the model without regulation, depending on the mean protein burst size.

The polarized state of light scattered by media provides much more characteristic information than the intensity alone. Thus, numerous polarimetric measurements are carried out to understand the media characteristics. Polarized radiative transfer is used to interpret these polarimetric measurements and obtain the media parameters, where the plane-parallel approximation model is usually adopted. Meanwhile, the graded-index phenomenon is widespread in nature, and the curved ray trajectory in graded-index media makes the computation of polarized radiative transfer more challenging. A suitable and effective numerical tool is of great value. In this work, we propose a lattice Boltzmann method (LBM) for plane-parallel polarized radiative transfer in graded-index media. The rigorous mathematical relation between the vector radiative-transfer equation and the LB model is proved. The Stokes vector can be obtained by the LB model through simple collision and streaming processes. Numerical tests show that the present LBM is effective and accurate for plane-parallel polarized radiative transfer in graded-index media, and also applicable to polarized radiative transfer in uniform refractive-index media under the plane-parallel approximation. Furthermore, we adopt the LBM to investigate the remote sensing problem of the atmosphere-ocean system with graded-index seawater, and find that the observed Stokes vector in the graded-index atmosphere-ocean system is markedly different from that in homogeneous system.

The problem of an optimal mapping between Hilbert spaces IN and OUT, based on a series of density matrix mapping measurements ${\rho }^{\left(l\right)}\to {\varrho }^{\left(l\right)}$, $l=1\cdots M$, is formulated as an optimization problem maximizing the total fidelity $\mathcal{F}={\sum }_{l=1}^M{\omega }^{\left(l\right)}F({\varrho }^{\left(l\right)},{\sum }_s{B}_s{\rho }^{\left(l\right)}{B}_s^{†})$ subject to probability preservation constraints on Kraus operators $B_s$. For $F(\varrho ,\sigma )$ in the form that total fidelity can be represented as a quadratic form with superoperator $\mathcal{F}={\sum }_s\langle B_s\left|S\right|B_s\rangle$ (either exactly or as an approximation) an iterative algorithm is developed. The work introduces two important generalizations of unitary learning: (1) IN/OUT states are represented as density matrices; (2) the mapping itself is formulated as a mixed unitary quantum channel $A^{OUT}={\sum }_s{\left|w_s\right|}^2{\mathcal{U}}_s{A}^{IN}{\mathcal{U}}_s^{†}$ (no general quantum channel yet). This marks a crucial advancement from the commonly studied unitary mapping of pure states ${\varphi }_l=\mathcal{U}{\psi }_l$ to a quantum channel, which allows us to distinguish probabilistic mixture of states and their superposition. An application of the approach is demonstrated on unitary learning of density matrix mapping ${\varrho }^{\left(l\right)}=\mathcal{U}{\rho }^{\left(l\right)}{\mathcal{U}}^{†}$, in this case a quadratic on $\mathcal{U}$ fidelity can be constructed by considering $\sqrt{{\rho }^{\left(l\right)}}\to \sqrt{{\varrho }^{\left(l\right)}}$ mapping, and on a quantum channel, where quadratic on $B_s$ fidelity is an approximation—a quantum channel is then obtained as a hierarchy of unitary mappings, a mixed unitary channel. The approach can be applied to studying quantum inverse problems, variational quantum algorithms, quantum tomography, and more. A software product implementing the algorithm is available from the authors.

Nematic liquid crystals confined to pi cells are known to exhibit a multistable electric behavior. As previous studies show, under an increasing electric field, nematics of rodlike molecules with their elastic constants related as $K_{22}$ (twist) $<K_{11}$ (splay) $<K_{33}$ (bend), undergo a continuous primary bifurcation at a critical voltage $U_{\mathrm{c}}$ from the bulk-planar state $H$ to the bulk-inclined state $I$, followed by a discontinuous transition into the bulk-vertical state $V$ above $U_{\mathrm{c}}$. On turning the field off, the $V$ state continuously transforms into a metastable π-twisted state $T$ that relaxes discontinuously to the $H$. The present study examines the evolution and relaxation behavior of Fréedericksz’s states in calamitic and bent-core nematics that differ significantly in their elastic anisotropy. Indeed, nematics with bent-shaped molecules present an anomalously low bend elastic constant, $K_{33}<K_{22}<K_{11}$. Our findings are the following: (a) The field-on sequence $\mathrm{H}\to \mathrm{I}\to \mathrm{V}$, as also the field-off sequence $\mathrm{V}\to \mathrm{T}\to \mathrm{H}$, remain common to both nematic types. (b) The two systems, however, differ in terms of the stability of the V state in a reducing field; in calamitics, the V geometry transforms discontinuously to the I above $U_{\mathrm{c}}$, and a second-order $\mathrm{I}\to \mathrm{H}$ change follows below $U_{\mathrm{c}}$; by contrast, in bent-core nematics, whether the core is flexible or rigid, the V state once formed remains stable at all voltages above $U_{\mathrm{c}}$, with the $\mathrm{V}\to \mathrm{T}\to \mathrm{H}$ transition taking place only below $U_{\mathrm{c}}$. The studies also include anisotropic propagation of fronts associated with the $\mathrm{T}\to \mathrm{H}$ transformation, pseudobiaxial conoscopic features of the reoriented states, periodic electric instabilities that differentiate the T and H geometries, and a comprison of computed and experimental results on cell capacitance and birefringence.

An analytical form has been derived using Ostrogradsky's integration method for the interaction between two thin rods of finite lengths in arbitrary relative configurations in a three-dimensional space, each treated as a line of point particles interacting through the Lennard-Jones 12-6 potential. Simplified analytical forms for coplanar, parallel, and collinear rods are also derived. Exact expressions for the force and torque between the rods are obtained. Similar results for a point particle interacting with a thin rod are provided. These interaction potentials can be widely used for analytical descriptions and computational modeling of systems involving rodlike objects such as liquid crystals, colloids, polymers, elongated viruses and bacteria, and filamentous materials including carbon nanotubes, nanowires, biological filaments, and their bundles.

We design 3D-printed motor-driven active particles and find that their dynamics can be characterized using the model of overdamped chiral active Brownian particles (ABPs), as demonstrated by measured angular statistics and translational mean squared displacements (MSDs). Furthermore, we propose a minimal model that reproduces the double-peak velocity distributions and further predicts a transition from the single-peak to the double-peak displacement distributions in short-time regimes. The model provides a clear physics picture of these phenomena, originating from the competition between the active motion and the translational diffusion. Our experiments confirm such picture. The minimal model enhances our understanding of activity-driven non-Gaussian phenomena. The designed particles could be further applied in the study of collective chiral motions.

We investigate the granular temperatures in force-free granular gases under exponential resetting. When a resetting event occurs, the granular temperature attains its initial value, whereas it decreases because of the inelastic collisions between the resetting events. We develop a theory and perform computer simulations for granular gas cooling in the presence of Poissonian resetting events. We also investigate the probability density function to quantify the distribution of granular temperatures. Our theory may help us to understand the behavior of nonperiodically driven granular systems.

We develop a model for two-layer traffic flow in which a batch of $n_o$ packets are dispatched from the source at regular intervals. This scenario is applicable in various communication and transportation systems, such as TCP congestion control mechanisms and congestion management through traffic lights. We demonstrate that implementing stochastic switching between the shortest-path and greedy approaches in the routing strategy of packet transmission results in a significant reduction in the total transmission weight when $n_o$ exceeds a certain threshold. This phenomenon mirrors Parrondo's paradox, in which two games or strategies, individually yielding losses, produce a winning outcome or optimal results when combined. In addition, we observe that the influence of layer 1 on overall dynamics surpasses that of layer 2. Furthermore, we find that the impact of the structural characteristics of layers is more significant for switching probability $\gamma <0.5$.

In this manuscript, we investigate the stochastic thermodynamics of Fisher information (FI), meaning we characterize both the fluctuations of FI, introducing a statistics of that quantity, and thermodynamic quantities. We introduce two initial conditions: an equilibrium initial condition and a minimum entropy initial condition, both under a protocol that drives the system to equilibrium. Its results indicate a dependence of the average FI on both the initial condition and path taken. Furthermore, the results indicate that the chosen parameter directly affects the FI of thermodynamic quantities, such as irreversible work and entropy, along with fluctuations of a stochastic FI. Last, we assess the further role of FI of the distribution of thermal quantities within the context of thermostatistical inequalities.

We use dynamic equations to derive a relation between correlation functions and response or relaxation functions in many-body systems. The relation is very general and holds both in equilibrium, when the usual fluctuation-dissipation theorem is valid, and to linear order in an expansion about arbitrary nonequilibrium states, when it is not. It provides a simple way to observe microscopic correlations via a system's macroscopic response, even in situations where the correlations are difficult to observe directly, and the response is not determined by the standard commutator (i.e., antisymmetrized) correlation functions. We illustrate our results by discussing fluids, both in equilibrium and nonequilibrium states, as well as several active-matter systems.

We empirically investigated how pedestrians rotate through bottlenecks to avoid collisions. Shoulder data was found to be more reliable and accurate for measuring rotation compared to head trajectories. An angle exceeding $30{}^{\circ }$ is used to identify the rotation state, with a false identification rate below 2.5%. Two types of rotation are observed: type I, where pedestrians actively rotate, gradually shifting their orientations away from the desired direction to adapt to confined space, and type II, where pedestrians rotate back. Statistical evidence indicates that the difference in blocking by opposite pedestrians and obstacles between the two sides of a square region in front of the pedestrian, is the potential mechanism triggering rotation behaviors, with a critical value of 20%. As blocking in that region and angular velocity increase, the rotation axis moves closer the pedestrian body center. The spatial distribution of rotation axes can be explained by the maximization of both short-term and long-term rotational yields. Additionally, in confined spaces, pedestrians need two or more step durations to complete the rotation, resulting in a longer rotation time. This paper enhances the understanding of the mechanisms behind human rotation through bottlenecks and provides empirical support for pedestrian rotation modeling.