The changeover from first-order to second-order phase transitions in $q$-state Potts models is obtained at $q_c=2$ in spatial dimension $d=3$ and essentially at $q_c=4$ in $d=2$, using a physically intuited simple adaptation of the Migdal-Kadanoff renormalization-group transformation. This simple procedure yields the latent heats at the first-order phase transitions. In both $d=2$ and 3, the calculated phase transition temperatures, respectively compared with the exact self-duality and Monte Carlo results, are dramatically improved. The method, when applied to a slab of finite thickness, yields dimensional crossover.

We study the nonequilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a fluid close to its bulk critical point. The average position of the particle initially displaced from the position of mechanical equilibrium is shown to feature long-time algebraic tails as the critical point of the field is approached, the universal exponents of which are determined in arbitrary spatial dimensions. As expected, this behavior cannot be captured by adiabatic approaches which assumes fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.

The nonequilibrium thermodynamics feature of a Brownian motor is investigated by obtaining exact time-dependent solutions. This in turn enables us to investigate not only the long time property (steady state) but also the short time the behavior of the system. The general expressions for the free energy, entropy production ${\dot{e}}_p\left(t\right)$ as well as entropy extraction ${\dot{h}}_d\left(t\right)$ rates are derived for a system that is genuinely driven out of equilibrium by time-independent force as well as by spatially varying thermal background. We show that for a system that operates between hot and cold reservoirs, most of the thermodynamics quantities approach a nonequilibrium steady state in the long time limit. The change in free energy becomes minimal at a steady state. However, for a system that operates in a heat bath where its temperature varies linearly in space, the entropy production and extraction rates approach a nonequilibrium steady state while the change in free energy varies linearly in space. This reveals that unlike systems at equilibrium, when systems are driven out of equilibrium, their free energy may not be minimized. The thermodynamic properties of a system that operates between the hot and cold baths are further compared and contrasted with a system that operates in a heat bath where its temperature varies linearly in space along with the reaction coordinate. We show that the entropy, entropy production, and extraction rates are considerably larger for the linearly varying temperature case than a system that operates between the hot and cold baths revealing such systems are inherently irreversible. For both cases, in the presence of load or when a distinct temperature difference is retained, the entropy $S\left(t\right)$ monotonously increases with time and saturates to a constant value as $t$ further steps up. The entropy production rate ${\dot{e}}_p$ decreases in time and at steady state, ${\dot{e}}_p={\dot{h}}_d>0$, which agrees with the results shown in M. Asfaw's [Phys. Rev. E 89, 012143 (2014); Phys. Rev. E 92, 032126 (2015)]. Moreover, the velocity, as well as the efficiency of the system that operates between the hot and cold baths, are also collated and contrasted with a system that operates in a heat bath where its temperature varies linearly in space along with the reaction coordinate. A system that operates between the hot and cold baths has significantly lower velocity but a higher efficiency in comparison with a linearly varying temperature case.

The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterize optimal thermodynamic distillation processes, and then we prove a relation between the amount of free energy dissipated in such processes and the free-energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or an arbitrary number of independent energy-incoherent systems, and they allow not only for a state transformation but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure, and thermodynamically free communication, up to second-order asymptotics in the number $N$ of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite $N$.

We report first-principles calculations of the triple point that allow us to predict the triple point temperature of atomic fluids to an accuracy that has not been previously possible. This is achieved by proposing a molecular simulation technique that can be used for solid-liquid equilibria at arbitrarily low pressures. It is demonstrated that the triple point is significantly influenced by the choice of two-body, three-body and quantum interactions. An improved theoretical understanding of triple points is important for both science in general, and metrology in particular, as it links the Boltzmann constant and the Kelvin temperature scale to fundamental constants.

We consider the parity-time (PT)-symmetric, nonlocal, nonlinear Schrödinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for the simplest graph topologies, such as star and tree graphs. The integrability of the problem is shown by proving the existence of an infinite number of conservation laws. A model for soliton generation in such PT-symmetric optical fibers and their networks governed by the nonlocal nonlinear Schrödinger equation is proposed. Exact formulas for the number of generated solitons are derived for the cases when the problem is integrable. Numerical solutions are obtained for the case when integrability is broken.

Attractor neural networks are one of the leading theoretical frameworks for the formation and retrieval of memories in networks of biological neurons. In this framework, a pattern imposed by external inputs to the network is said to be learned when this pattern becomes a fixed point attractor of the network dynamics. The storage capacity is the maximum number of patterns that can be learned by the network. In this paper, we study the storage capacity of fully connected and sparsely connected networks with a binarized Hebbian rule, for arbitrary coding levels. Our results show that a network with discrete synapses has a similar storage capacity as the model with continuous synapses, and that this capacity tends asymptotically towards the optimal capacity, in the space of all possible binary connectivity matrices, in the sparse coding limit. We also derive finite coding level corrections for the asymptotic solution in the sparse coding limit. The result indicates the capacity of networks with Hebbian learning rules converges to the optimal capacity extremely slowly when the coding level becomes small. Our results also show that in networks with sparse binary connectivity matrices, the information capacity per synapse is larger than in the fully connected case, and thus such networks store information more efficiently.

Many animals and robots move using undulatory motion of their bodies. When the bodies are in close proximity undulatory motion can lead to novel collective behavior such as gait synchronization, spatial reconfiguration, and clustering. Here we study the role of contact interactions between model undulatory swimmers: three-link robots in experiment and multilink swimmers in simulation. The undulatory gait of each swimmer is generated through a time-dependent sinusoidal-like waveform which has a fixed phase offset, $\varphi$. By varying the phase relationship between neighboring swimmers we seek to study how contact forces and planar configurations are governed by the phase difference between neighboring swimmers. We find that undulatory actuation in close proximity drives neighboring swimmers into planar equilibrium configurations that depend on the actuation phase difference. We propose a model for stable planar configurations of nearest-neighbor undulatory swimmers which we call the gait compatibility condition, which is the set of planar and phase configurations in which no collisions occur. Robotic experiments with two, three, and four swimmers exhibit good agreement with the compatibility model. To study the contact forces and the time-averaged equilibrium between undulatory systems we perform simulations. To probe the interaction potential between undulatory swimmers we apply a small force to each swimmer longitudinally to separate them from the compatible configuration and we measure their steady-state displacement. These studies reveal that undulatory swimmers in close proximity exhibit attractive longitudinal interaction forces that drive the swimmers from incompatible to compatible configurations. This system of undulatory swimmers provides new insight into active-matter systems which move through body undulation. In addition to the importance of velocity and orientation coherence in active-matter swarms, we demonstrate that undulatory phase coherence is also important for generating stable, cohesive group configurations.

Mixtures of active and passive particles are predicted to exhibit a variety of nonequilibrium phases. Here we report a dynamic clustering phase in mixtures of colloids and motile bacteria. We show that colloidal clustering results from a balance between bond breaking due to persistent active motion and bond stabilization due to torques that align active particle velocity tangentially to the passive particle surface. Furthermore, dynamic clustering spans a broad regime between diffusivity-based and motility-induced phase separation that subsumes typical bacterial motility parameters.

An analytical model for predicting the competitive evaporation of two and three sessile drops is proposed, based on an analytical solution, in terms of Mehler functions, of the steady species and energy conservation equations for the gaseous phase. The assessment through a comparison with accurate numerical solutions of the species conservation equations is reported in order to quantify the accuracy of the analytical solution. The model is validated against three available sets of experiments on two and three sessile drops on a line array. The decrease of the evaporation rate caused by the vicinity of sessile drops is reported in terms of a screening coefficient given by a relatively simple analytical expression. The influence of wall wettability on the evaporation of pairs of sessile drops is analyzed, and a parameter is proposed to quantify the effect of geometry in a unified way.

We consider an elastic helical medium whose tensor stiffness twirls uniformly along the helix axis. We are interested in analyzing the band structure when the whole material is externally forced to rotate around the helix axis to a fixed constant frequency. Departing from a general dynamic description of the elastic phenomena, we establish a set of equations for the displacement vector and the stress tensor. These equations allow us to calculate the band structure parametrized by the externally imposed rotating frequency. We find that the band structure strongly depends on the rotation frequency, and we show that backward and forward modes propagate differently, particularly for the longitudinal and right-polarized modes.

Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain $\overline{r}$ normalized by the averaged distance between centers of the adjacent droplets $\overline{l}$ scales as $\overline{r}/\overline{l}\sim n^{0.76}$, where $n$ is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit. The values of the dimensionless Kuhn length $\tilde{b}\cong 2.12\pm 0.015$ and of the averaged absolute value of the bond angle of the droplet chains $\overline{\left|\theta \right|}=22.0\pm 0.5^0$ are determined. Using these values we demonstrate that the predictions of the Kramers theorem for the gyration radius of branched polymers are valid also for the branched droplets' chains. We discuss physical interactions that explain both the high value of the power exponent and the applicability of the Kramers theorem including the effects of the excluded volume, surrounding droplet monomers, and the prohibition of extreme values of the bond angle.

Ultrafast water transport in carbon nanotubes (CNTs) has drawn a great deal of attention in a number of applications, such as water desalination, power generation, and biomolecule detection. With the recent experimental advances in water filling of isolated CNTs, the Lucas-Washburn theory for capillary rise in tubes needs to be revisited for a better understanding of the physics and dynamics of water filling in CNTs. Here, the Lucas-Washburn theory is corrected for the hydrodynamic entrance effects as well as the variation of capillary pressure and hydrodynamic properties with the radius and length of CNTs. Due to the large slippage in CNTs, inclusion of the entrance effects is important particularly for the initial stages of filling where a $L\propto t$ scaling, as opposed to $L^2\propto t$, is observed in our molecular dynamics (MD) simulations. The corrected Lucas-Washburn theory is shown to predict the water filling dynamics in CNTs as observed in MD simulations. With the corrected theory, we achieve a better understanding of capillary rise and water filling dynamics in CNTs.

We develop an algorithm suitable for parallel molecular dynamics simulations in $d$ spatial dimensions and describe its implementation in $\mathrm{C}++$. All routines work in arbitrary $d$; the maximum simulated $d$ is limited only by available computing resources. These routines include several that are particularly useful for studies of the glass-jamming transition, such as SWAP Monte Carlo and FIRE energy minimization. The scalings of simulation runtimes with the number of particles $N$ and number of simulation threads $n_{\mathrm{threads}}$ are comparable to popular molecular dynamics codes such as LAMMPS. The efficient parallel implementation allows simulation of systems that are much larger than those employed in previous high-dimensional glass-transition studies. As a demonstration of the code's capabilities, we show that supercooled $d=6$ liquids can possess dynamics that are substantially more heterogeneous and experience a breakdown of the Stokes-Einstein relation that is substantially stronger than previously reported, owing at least in part to the much smaller system sizes employed in earlier simulations.

We discuss results on the dynamics of thermalization for a model with Gaussian interactions between two classical many-body systems trapped in external harmonic potentials. Previous work showed an approximate power-law scaling of the interaction energy with the number of particles, with particular focus on the dependence of the anomalous exponent on the interaction strength. Here we explore the role of the interaction range in determining anomalous exponents, showing that it is a more relevant parameter to differentiate distinct regimes of responses of the system. More specifically, on varying the interaction range from its largest values while keeping the interaction strength constant, we observe a crossover from an integrable system, approximating the Caldeira-Leggett interaction term in the long-range limit, to an intermediate interaction range in which the system manifests anomalous scaling, and finally to a regime of local interactions in which anomalous scaling disappears. A Fourier analysis of the interaction energy shows that nonlinearities give rise to an effective bath with a broad band of frequencies, even when starting with only two distinct trapping frequencies, yielding efficient thermalization in the intermediate regime of interaction range. We provide qualitative arguments, based on an analogous Fourier analysis of the standard map, supporting the view that anomalous scaling and features of the Fourier spectrum may be used as proxies to identify the role of chaotic dynamics. Our work, that encompasses models developed in different contexts and unifies them in a common framework, may be relevant to the general understanding of the role of nonlinearities in a variety of many-body classical systems, ranging from plasmas to trapped atoms and ions.

We propose a systematic method based on reinforcement learning (RL) techniques to find the optimal path to minimize the total entropy production between two equilibrium states of open systems at the same temperature in a given fixed period. Benefiting from the generalization of the deep RL techniques, we provide a powerful tool to address this problem in quantum systems even with two-dimensional continuous controllable parameters. We successfully apply our method to the classical and quantum two-level systems.

We study the effect of group interactions on the emergence of consensus in a spin system. Agents with discrete opinions $\{0,1\}$ form groups. They can change their opinion based on their group's influence (voter dynamics), but groups can also split and merge (adaptation). In a hypergraph, these groups are represented by hyperedges of different sizes. The heterogeneity of group sizes is controlled by a parameter $\beta$. To study the impact of $\beta$ on reaching consensus, we provide extensive computer simulations and compare them with an analytic approach for the dynamics of the average magnetization. We find that group interactions amplify small initial opinion biases, accelerate the formation of consensus, and lead to a drift of the average magnetization. The conservation of the initial magnetization, known for basic voter models, is no longer obtained.

A basic question in network community detection is how modular a given network is. This is usually addressed by evaluating the quality of partitions detected in the network. The Girvan-Newman (GN) modularity function is the standard way to make this assessment, but it has a number of drawbacks. Most importantly, it is not clearly interpretable, given that the measure can take relatively large values on partitions of random networks without communities. Here we propose a measure based on the concept of robustness: modularity is the probability to find trivial partitions when the structure of the network is randomly perturbed. This concept can be implemented for any clustering algorithm capable of telling when a group structure is absent. Tests on artificial and real graphs reveal that robustness modularity can be used to assess and compare the strength of the community structure of different networks. We also introduce two other quality functions: modularity difference, a suitably normalized version of the GN modularity, and information modularity, a measure of distance based on information compression. Both measures are strongly correlated with robustness modularity, but have lower time complexity, so they could be used on networks whose size makes the calculation of robustness modularity too costly.

Pulsed excitations of piezoelectric transducers affect during the buildup the force contributions from acoustic streaming (AS) and the acoustic radiation force (ARF) to the total force in a standing pressure wave differently. We find with an optical tweezer as measuring instrument that during the first 120 000 excitation periods and across different pulsing frequencies, the AS-induced displacement is on average less than 20% of its nonpulsed value for a duty cycle of 50%, whereas the ARF-induced displacement is around 50%. These findings show that a pulsed excitation can be a tool for reducing AS compared to the ARF.