Understanding the thermodynamic role of measurement in quantum mechanical systems is a burgeoning field of study. In this article, we study a double quantum dot (DQD) connected to two macroscopic fermionic thermal reservoirs. We assume that the DQD is continuously monitored by a quantum point contact (QPC), which serves as a charge detector. Starting from a minimalist microscopic model for the QPC and reservoirs, we show that the local master equation of the DQD can alternatively be derived in the framework of repeated interactions and that this framework guarantees a thermodynamically consistent description of the DQD and its environment (including the QPC). We analyze the effect of the measurement strength and identify a regime in which particle transport through the DQD is both assisted and stabilized by dephasing. We also find that in this regime the entropic cost of driving the particle current with fixed relative fluctuations through the DQD is reduced. We thus conclude that under continuous measurement a more constant particle current may be achieved at a fixed entropic cost.

In this paper, an approach to the disease transmission dynamic of a coronavirus pandemic is presented. Compared to models commonly known from the literature, new classes that describe this dynamic to our model were added, which are a class representing costs of the pandemic and a class of the individuals being vaccinated but without antibodies. Parameters which at most of them depend on time were used. Sufficient conditions for a dual $\varepsilon$-closed-loop Nash equilibrium in the form of the verification theorem are formulated. A numerical algorithm and numerical example are constructed.

We study the equilibrium density profile of particles in two one-dimensional classical integrable models, namely hard rods and the hyperbolic Calogero model, placed in confining potentials. For both of these models the interparticle repulsion is strong enough to prevent particle trajectories from intersecting. We use field theoretic techniques to compute the density profile and their scaling with system size and temperature, and we compare them with results from Monte Carlo simulations. In both cases we find good agreement between the field theory and simulations. We also consider the case of the Toda model in which interparticle repulsion is weak and particle trajectories can cross. In this case, we find that a field theoretic description is ill-suited and instead, in certain parameter regimes, we present an approximate Hessian theory to understand the density profile. Our work provides an analytical approach toward understanding the equilibrium properties for interacting integrable systems in confining traps.

Nonequilibrium and instability features of prey-predator-like systems associated to topological quantum domains emerging from a quantum phase-space description are investigated in the framework of the Weyl-Wigner quantum mechanics. Reporting about the generalized Wigner flow for one-dimensional Hamiltonian systems, $\mathcal{H}(x,k)$, constrained by ${\partial }^2\mathcal{H}/\partial x\partial k=0$, the prey-predator dynamics driven by Lotka-Volterra (LV) equations is mapped onto the Heisenberg-Weyl noncommutative algebra, $[x,k]=i$, where the canonical variables $x$ and $k$ are related to the two-dimensional LV parameters, $y=e^{-x}$ and $z=e^{-k}$. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters for the prey-predator-like dynamics are then shown to be affected by quantum distortions over the classical background, in correspondence with nonstationarity and non-Liouvillianity properties quantified in terms of Wigner currents and Gaussian ensemble parameters. As an extension, considering the hypothesis of discretizing the time parameter, nonhyperbolic bifurcation regimes are identified and quantified in terms of $z-y$ anisotropy and Gaussian parameters. The bifurcation diagrams exhibit, for quantum regimes, chaotic patterns highly dependent on Gaussian localization. Besides exemplifying a broad range of applications of the generalized Wigner information flow framework, our results extend, from the continuous (hyperbolic regime) to discrete (chaotic regime) domains, the procedure for quantifying the influence of quantum fluctuations over equilibrium and stability scenarios of LV driven systems.

The effects of inertia in active matter and motility-induced phase separation (MIPS) have attracted growing interest but still remain poorly studied. We studied MIPS behavior in the Langevin dynamics across a broad range of particle activity and damping rate values with molecular dynamic simulations. Here we show that the MIPS stability region across particle activity values consists of several domains separated by discontinuous or sharp changes in susceptibility of mean kinetic energy. These domain boundaries have fingerprints in the system's kinetic energy fluctuations and characteristics of gas, liquid, and solid subphases, such as the number of particles, densities, or the power of energy release due to activity. The observed domain cascade is most stable at intermediate damping rates but loses its distinctness in the Brownian limit or vanishes along with phase separation at lower damping values.

We analyze the phase diffusion, quantum fluctuations and their spectral features of a one-dimensional Bose-Josephson junction (BJJ) nonlinearly coupled to a bosonic heat bath. The phase diffusion is considered by taking into account of random modulations of the BJJ modes causing a phase loss of initial coherence between the ground and excited states, whereby the frequency modulation is incorporated in the system-reservoir Hamiltonian by an interaction term linear in bath operators but nonlinear in system (BJJ) operators. We examine the dependence of the phase diffusion coefficient on the on-site interaction and temperature in the zero- and $\pi$-phase modes and demonstrate its phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes in the $\pi$-phase mode. Based on the thermal canonical Wigner distribution, which is the equilibrium solution of the associated quantum Langevin equation for phase, coherence factor is calculated to study phase diffusion for the zero- and $\pi$-phase modes. We investigate the quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra which capture an interesting shift in Josephson frequency induced by frequency fluctuation due to nonlinear system-reservoir coupling, as well as the on-site interaction-induced splitting in the weak dissipative regime.

Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and immobile excitations' dubbed fractons. Unfortunately, such systems have so far escaped a complete macroscopic formulation as viscous fluids. In this work, we construct a consistent hydrodynamic description for fluids invariant under translation, rotation, and dipole shift symmetry. We use symmetry principles to formulate a thermodynamic theory for dipole-conserving systems at equilibrium and apply irreversible thermodynamics in order to elucidate dissipative effects. Remarkably, we find that the inclusion of the energy conservation not only renders the longitudinal modes diffusive rather than subdiffusive but also diffusion is present even at the lowest order in the derivative expansion. This work paves the way towards an effective description of many-body systems with constrained dynamics such as ensembles of topological defects, fracton phases of matter, and certain models of glasses.

Excitable photonic systems show promise for ultrafast analog computation, several orders of magnitude faster than biological neurons. Optically injected quantum dot lasers display several excitable mechanisms with dual-state quantum lasers recently emerging as true all-or-none excitable artificial neurons. For use in applications, deterministic triggering is necessary and this has previously been demonstrated in the literature. In this work we analyze the crucially important refractory time for this dual-state system, which defines the minimum time between distinct pulses in any train.

In the present work we explore the concept of solitary wave billiards. That is, instead of a point particle, we examine a solitary wave in an enclosed region and examine its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. Furthermore, the nature of the scattering of the deformable solitary wave particle is elucidated on the basis of a negative Goos-Hänchen effect which, in addition to a trajectory shift, also results in an effective shrinkage of the billiard domain.

The renormalization group is a set of tools that can be used to incorporate the effect of fluctuations in a dynamical system as a rescaling of the system's parameters. Here, we apply the renormalization group to a pattern-forming stochastic cubic autocatalytic reaction-diffusion model and compare its predictions with numerical simulations. Our results demonstrate a good agreement within the range of validity of the theory and show that external noise can be used as a control parameter in such systems.

Standing and moving discrete breathers (or equally, intrinsic localized modes) in a square $\beta$-Fermi-Pasta-Ulam-Tsingou lattice are obtained by applying localizing functions to the delocalized nonlinear vibrational modes (DNVMs) found earlier by Ryabov and Chechin. The initial conditions used in our study do not correspond to exact spatially localized solutions, but make it possible to obtain long-lived quasibreathers. The approach employed in this work can easily be used to search for quasibreathers in three-dimensional crystal lattices, for which DNVMs with frequencies outside the phonon spectrum are known.

A common problem in time-series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens' theorem proves a time-delayed embedding of the partial state is diffeomorphic to the attractor, although for chaotic and highly nonlinear systems, learning these delay coordinate mappings is challenging. We utilize deep artificial neural networks (ANNs) to learn discrete time maps and continuous time flows of the partial state. Given training data for the full state, we also learn a reconstruction map. Thus, predictions of a time series can be made from the current state and several previous observations with embedding parameters determined from time-series analysis. The state space for time evolution is of comparable dimension to reduced order manifold models. These are advantages over recurrent neural network models, which require a high-dimensional internal state or additional memory terms and hyperparameters. We demonstrate the capacity of deep ANNs to predict chaotic behavior from a scalar observation on a manifold of dimension three via the Lorenz system. We also consider multivariate observations on the Kuramoto-Sivashinsky equation, where the observation dimension required for accurately reproducing dynamics increases with the manifold dimension via the spatial extent of the system.

Biological flow networks adapt their network morphology to optimize flow while being exposed to external stimuli from different spatial locations in their environment. These adaptive flow networks retain a memory of the stimulus location in the network morphology. Yet, what limits this memory and how many stimuli can be stored are unknown. Here, we study a numerical model of adaptive flow networks by applying multiple stimuli subsequently. We find strong memory signals for stimuli imprinted for a long time into young networks. Consequently, networks can store many stimuli for intermediate stimulus duration, which balance imprinting and aging.

Attractive colloids diffuse and aggregate to form gels, solidlike particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever-decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.

We study the self-organization in a monolayer (a two-dimensional system) of flexible planar trimer particles. The molecules are made up of two mesogenic units linked by a spacer, all of which are modeled as hard needles of the same length. Each molecule can dynamically adopt two conformational states: an achiral bent-shaped (cis-) and a chiral zigzag (trans-) one. Using constant pressure Monte Carlo simulations and Onsager-type density functional theory (DFT), we show that the system consisting of these molecules exhibits a rich spectrum of liquid crystalline phases. The most interesting observation is the identification of stable smectic splay-bend ($S_{\mathrm{SB}}$) and chiral smectic-$A$ ($S_A^{*}$) phases. The $S_{\mathrm{SB}}$ phase is also stable in the limit, where only $cis$- conformers are allowed. The second phase that occupies a considerable portion of the phase diagram is $S_A^{*}$ with chiral layers, where the chirality of the neighboring layers is of opposite sign. The study of the average fractions of the trans- and cis- conformers in various phases shows that while in the isotropic phase all fractions are equally populated, the $S_A^{*}$ phase is dominated by chiral conformers (zigzag), but the achiral conformers win in the smectic splay-bend phase. To clarify the possibility of stabilization of the nematic splay-bend ($N_{\mathrm{SB}}$) phase for trimers, the free energy of the $N_{\mathrm{SB}}$ and $S_{\mathrm{SB}}$ phases is calculated within DFT for the cis- conformers, for densities where simulations show stable $S_{\mathrm{SB}}$. It turns out that the $N_{\mathrm{SB}}$ phase is unstable away from the phase transition to the nematic phase, and its free energy is always higher than that of $S_{\mathrm{SB}}$, down to the transition to the nematic phase, although the difference in free energies becomes extremely small when approaching the transition.

We have assessed the assumption of local thermodynamic equilibrium in a shock wave by comparing local thermodynamic data generated with nonequilibrium molecular dynamics (NEMD) simulations with results from corresponding equilibrium simulations. The shock had a Mach number approximately equal to 2 in a Lennard-Jones spline liquid. We found that the local equilibrium assumption holds perfectly well behind the wave front, and is a very good approximation in the front itself. This was supported by calculations of the excess entropy production in the shock front with four different methods that use the local equilibrium assumption in different ways. Two of the methods assume local equilibrium between excess thermodynamic variables by treating the shock as an interface in Gibbs's sense. The other two methods are based on the local equilibrium assumption in a continuous description of the shock front. We show for the shock studied in this work that all four methods give excess entropy productions that are in excellent agreement, with an average variance of 3.5% for the nonequilibrium molecular dynamics (NEMD) simulations. In addition, we solved the Navier-Stokes (N-S) equations numerically for the same shock wave using an equilibrium equation of state (EoS) based on a recently developed perturbation theory. The results for the density, pressure, and temperature profiles agree well with the profiles from the NEMD simulations. For instance, the shock waves generated in the two simulations travel with almost the same speed; the average absolute Mach-number deviation of the N-S simulations relative to NEMD is 2.6% in the investigated time interval.

We study the collective phenomena and constraints associated with the aggregation of individual cooling units from a statistical mechanics perspective. These units are modeled as thermostatically controlled loads (TCLs) and represent zones in a large commercial or residential building. Their energy input is centralized and controlled by a collective unit—the air handling unit (AHU)—delivering cool air to all TCLs, thereby coupling them together. Aiming to identify representative qualitative features of the AHU-to-TCL coupling, we build a simple but realistic model and analyze it in two distinct regimes: the constant supply temperature (CST) and the constant power input (CPI) regimes. In both cases, we center our analysis on the relaxation dynamics of individual TCL temperatures to a statistical steady state. We observe that while the dynamics are relatively fast in the CST regime, resulting in all TCLs evolving around the control set point, the CPI regime reveals the emergence of a bimodal probability distribution and two, possibly strongly separated, timescales. We observe that the two modes in the CPI regime are associated with all TCLs being in the same low or high airflow states, with an occasional collective transition between the modes akin to Kramer's phenomenon in statistical physics. To the best of our knowledge, this phenomenon has been overlooked in building energy systems despite its direct operational implications. It highlights a trade-off between occupational comfort—related to zonal temperature variations—and energy consumption.

The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be attributed to individual ions. Here I demonstrate that although the total wall force balances the bulk osmotic pressure as required by mechanical equilibrium, the individual partial osmotic pressures are extrathermodynamic quantities dependent on the electrical structure at the wall, and as such they resemble attempts to define individual ion activity coefficients. The limiting case where the wall is a barrier to only one species of ion is also considered, and with ions on both sides the classic Gibbs-Donnan membrane equilibrium is recovered, thus providing a unifying treatment. The analysis can be extended to illustrate how the electrical state of the bulk is affected by the nature of the walls and the container handling history, thus supporting the “Gibbs-Guggenheim uncertainty principle,” namely the notion that the electrical state is unmeasurable and usually accidentally determined. Since this uncertainty is conferred also onto individual ion activities, it has implications for the current (2002) IUPAC definition of $p\text{H}$.

We report phase separation in a mixture of “hot” and “cold” three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of “hot” and “cold” dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity $\chi$ of the system. From constant density simulations of symmetric dumbbells, we observe that the “hot” and “cold” dumbbells phase separate at higher activity ratio $(\chi >5.80)$ compared to that of a mixture of hot and cold Lennard-Jones monomers $(\chi >3.44)$. We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.