Fluctuations of dynamical quantities are fundamental and inevitable. For the booming research in nanotechnology, huge relative fluctuation comes with the reduction of system size, leading to large uncertainty for the estimates of dynamical quantities. Thus, increasing statistical efficiency, i.e., reducing the number of samples required to achieve a given accuracy, is of great significance for accurate estimation. Here we propose a theory as a fundamental solution for such problem by constructing auxiliary path for each real path. The states on auxiliary paths constitute canonical ensemble and share the same macroscopic properties (NVT) with the initial states of the real path. By implementing the theory in molecular dynamics simulations, we obtain a nanoscale Couette flow field with an accuracy of $0.2\mu \mathrm{m}/\mathrm{s}$ with relative standard error $<0.1$. The required number of samples is reduced by 12 orders compared to conventional method. The predicted thermolubric behavior of water sliding on a self-assembled surface is directly validated by experiment under the same velocity. This theory only assumes the system is initially in thermal equilibrium, then driven from that equilibrium by an external perturbation. It could serve as a general approach for extracting the accurate estimate of dynamical quantities from large fluctuations to provide insights on atomic level under experimental conditions, and benefit the studies on mass transport through (biological) nanochannels and fluid film lubrication of nanometer thickness.

The Bohr-Van Leeuwen theorem states that an external static magnetic field does not influence the state of a classical equilibrium system: There is no equilibrium classical magnetism, since the magnetic field does not do work. We revisit this famous no-go result and consider a classical charged Brownian particle interacting with an equilibrium bath. We confirm that the Bohr-Van Leeuwen theorem holds for the long-time (equilibrium) state of the particle. But the external static, homogeneous magnetic field does influence the long-time state of the thermal bath, which is described via the Caldeira-Leggett model. In particular, the magnetic field induces an average angular momentum for the (uncharged) bath, which separates into two sets rotating in opposite directions. The effect relates to the bath going slightly out of equilibrium under the influence of the Brownian particle and persists for arbitrarily long times. In this context we studied the behavior of the two other additive integrals of motion, energy, and linear momentum. The situation with linear momentum is different, because it is dissipated away by (and from) the bath modes. The average energy of the bath mode retains the magnetic field as a small correction. Thus, only the bath angular momentum really feels the magnetic field for long times.

The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite-size effects and criticality in the three-dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable “condensed” nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function, and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.

The present work investigates the effect of inertia on the entropy production rate $\mathrm{\Pi }$ for all canonical models of active particles for different dimensions and the type of confinement. To calculate $\mathrm{\Pi }$, the link between the entropy production and dissipation of heat rate is explored, resulting in a simple and intuitive expression. By analyzing the Kramers equation, alternative formulations of $\mathrm{\Pi }$ are obtained and the virial theorem for active particles is derived. Exact results are obtained for particles in an unconfined environment and in a harmonic trap. In both cases, $\mathrm{\Pi }$ is independent of temperature. For the case of a harmonic trap, $\mathrm{\Pi }$ attains a maximal value for $\tau ={\omega }^{-1}$, where $\tau$ is the persistence time and $\omega$ is the natural frequency of an oscillator. For active particles in one-dimensional box, or other nonharmonic potentials, thermal fluctuations are found to reduce $\mathrm{\Pi }$.

We study the nanoscale patterns that form on the surface of a rotating sample of an elemental material that is bombarded with a broad noble gas ion beam for angles of incidence $\theta$ just above the critical angle for pattern formation ${\theta }_c$. The pattern formation depends crucially on the ion energy $E$. In simulations carried out in the low-energy regime in which sputtering is negligible, we find disordered arrays of nanoscale mounds (nanodots) that coarsen in time. Disordered arrays of nanodots also form in the high-energy regime in which there is substantial sputtering, but no coarsening occurs close to the threshold angle. Finally, for values of $E$ just above the sputter yield threshold, nanodot arrays with an extraordinary degree of hexagonal order emerge for a range of parameter values, even though there is a broad band of linearly unstable wavelengths. This finding might prove to be useful in applications in which highly ordered nanoscale patterns are needed.

Fluid-fluid interfaces, laden with polymers, surfactants, lipid bilayers, proteins, solid particles, or other surface-active agents, often exhibit a rheologically complex response to deformations. Despite its academic and practical relevance to fluid dynamics and various other fields of research, the role of interfacial rheology in viscous fingering remains fairly underexplored. A noteworthy exception is the work by Li and Manikantan [Phys. Rev. Fluids 6, 074001 (2021)], who used linear stability analysis to show that surface rheological stresses act to stabilize the development of radial viscous fingering at the linear regime. In this paper, we perform a perturbative, second-order mode-coupling analysis of the system and investigate the influence of interfacial rheology on the morphology of the fingering structures at early nonlinear stages of the dynamics. In particular, we focus on understanding how interfacial rheology impacts the emblematic finger tip-widening and finger tip-splitting phenomena that take place in radial viscous fingering in Hele-Shaw cells. We describe the viscous Newtonian fluid-fluid interface by using a Boussinesq-Scriven model, and derive a generalized Young-Laplace pressure jump condition at the fluid-fluid interface. In this framing, we go beyond the purely linear description and use Darcy's law to obtain a perturbative mode-coupling differential equation which describes the time evolution of the perturbation amplitudes, accurate to second order. Our early nonlinear mode-coupling results indicate that regardless of their stabilizing action at the linear regime, interfacial rheology effects favor finger tip widening, leading to the occurrence of enhanced finger tip-splitting events.

Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad hoc without a clear physical explanation. We investigated data-driven models theoretically on a linear system. We argue that these models are equivalent to nonlinear length scale scaling laws of transport coefficients. The equivalence to scaling laws justified the physical plausibility and revealed the limitation of data-driven models. Our argument also points out that modeling the scaling law could avoid practical difficulties in data-driven models like derivative estimation and variable selection on noisy data. We further proposed a constitutive relation model based on scaling law and tested it on the calculation of Rayleigh scattering spectra. The result shows our data-driven model has a clear advantage over the Chapman-Enskog expansion and moment methods.

Higher intensity of strong-coupling stimulated Brillouin scattering (SC-SBS) amplification is achieved by supplementary Raman amplification. In this scheme, a Raman pump laser first amplifies the seed pulse in the homogeneous plasma, and then a SC-SBS pump laser continues the amplification in the inhomogeneous plasma in order to suppress the spontaneous instability of pump lasers. The intensity of the seed laser gets higher and the duration of the seed laser gets shorter than that in the pure SC-SBS scheme with the same incident energy, while the energy conversion efficiency is not significantly reduced. We also found that the SC-SBS amplification is seeded by the leading pulse of Raman amplification. The results obtained from envelope coupling equations, Vlasov simulations, and two-dimensional particle-in-cell simulations agree with each other. This scheme offers a possible way to improve the SC-SBS amplification in experiments.

Saturable absorption is a nonlinear effect where a material's ability to absorb light is frustrated due to a high influx of photons and the creation of electron vacancies. Experimentally induced saturable absorption in copper revealed a reduction in the temporal duration of transmitted x-ray laser pulses, but a detailed account of changes in opacity and emergence of resonances is still missing. In this computational work, we employ nonlocal thermodynamic equilibrium plasma simulations to study the interaction of femtosecond x rays and copper. Following the onset of frustrated absorption, we find that a $K\text{–}M$ resonant transition occurring at highly charged states turns copper opaque again. The changes in absorption generate a transient transparent window responsible for the shortened transmission signal. We also propose using fluorescence induced by the incident beam as an alternative source to achieve shorter x-ray pulses. Intense femtosecond x rays are valuable to probe the structure and dynamics of biological samples or to reach extreme states of matter. Shortened pulses could be relevant for emerging imaging techniques.

The free-energy model can extend the lattice Boltzmann method to multiphase systems. However, there is a lack of models capable of simulating multicomponent multiphase fluids with partial miscibility. In addition, existing models cannot be generalized to honor thermodynamic information provided by any multicomponent equation of state of choice. In this paper, we introduce a free-energy lattice Boltzmann model where the forcing term is determined by the fugacity of the species, the thermodynamic property that connects species partial pressure to chemical potential calculations. By doing so, we are able to carry out multicomponent multiphase simulations of partially miscible fluids and generalize the methodology for use with any multicomponent equation of state of interest. We test this fugacity-based lattice Boltzmann method for the cases of vapor-liquid equilibrium for two- and three-component mixtures in various temperature and pressure conditions. We demonstrate that the model is able to reliably reproduce phase densities and compositions as predicted by multicomponent thermodynamics and can reproduce different characteristic pressure-composition and temperature-composition envelopes with a high degree of accuracy. We also demonstrate that the model can offer accurate predictions under dynamic conditions.

We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large deviation functions for an initial step density profile with the fluctuating (annealed) and the fixed (quenched) initial conditions. These hydrodynamic results are applicable for a general single-file system and they agree with recent exact results obtained by microscopic solutions for specific model systems.

When a fluctuating system is subjected to a time-dependent drive or nonconservative forces, the direct-inverse symmetry of the dynamics can be broken so inducing an average bias. Here we start from the fluctuation theorem, a cornerstone of stochastic thermodynamics, for inspecting the unbalancing between direct and inverse dynamical outputs, here called “events,” in a bidirectional forward-backward setup. The occurrence of an event might correspond to the realization of a quantitative output, or to the realization of a sequence of acts that compose a complex “narrative.” The focus is on mutual bounds between the probabilities of occurrence of direct and inverse events in the forward and backward mode. The inspection is made for systems in contact with a thermal bath, and by assuming Markov dynamics on the uncontrolled degrees of freedom. The approach comprises both the case of systems under a time-dependent drive and time-independent external forces. The general formulation is then used to derive (or re-derive) specialized results valid for finite-time processes, and for systems taken into steady conditions (either periodic steady states or steady states) starting from equilibrium. Among the results, we find already known forms of “generalized” thermodynamic uncertainty relations, and derive useful constraints concerning the work distribution function for systems in steady conditions.

We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, $\mathcal{S}$, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part $\mathcal{E}$, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem $\mathcal{S}$ under scrutiny, and the other one with the environment $\mathcal{E}$. We investigate the behavior of $\mathcal{S}$ at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a quench of the coupling between $\mathcal{S}$ and $\mathcal{E}$. When $\mathcal{S}$ develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of $\mathcal{E}$, whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of $\mathcal{E}$, are observed for the decoherence of the subsystem $\mathcal{S}$, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with $\mathcal{E}$.

We show that homogeneous and nonhomogeneous states of the one-dimensional self-gravitating sheets models have different ergodic properties. The former are nonergodic and the one-particle distribution function has a zero collision term if a proper limit is taken for the periodic boundary conditions. As a consequence, homogeneous states of the sheets model are nonergodic and do not relax to the equilibrium state, while nonhomogeneous states are ergodic in a time window of the order of the relaxation time to equilibrium, as similarly observed in other systems with a long range interaction.

Using the transfer matrix technique, we estimate the entropy for a gas of rods of sizes equal to $k$ (named $k$-mers), which cover completely a square lattice. Our calculations were made considering three different constructions, using periodical and helical boundary conditions. One of those constructions, which we call profile method, was based on the calculations performed by Dhar and Rajesh to obtain a lower limit to the entropy of very large chains placed on the square lattice. This method, so far as we know, was never used before to define the transfer matrix, but turned out to be very useful, since it produces matrices with smaller dimensions than those obtained using the usual approach. Our results were obtained for chain sizes ranging from $k=2$ to $k=10$ and they are compared with results already available in the literature. In the case of dimers ($k=2$) our results are compatible with the exact result. For trimers ($k=3$), recently investigated by Ghosh et al., also our results were compatible, with the same happening for the simulational estimates obtained by Pasinetti et al. in the whole range of rod sizes. Our results are also consistent with the asymptotic expression for the behavior of the entropy as a function of the size $k$, proposed by Dhar and Rajesh for very large rods ($k\gg 1$).

Nematic ordering, where the spins globally align along a spontaneously chosen axis irrespective of direction, occurs in spin-glass systems of classical Heisenberg spins in $d=3$. In this system where the nearest-neighbor interactions are quenched randomly ferromagnetic or antiferromagnetic, instead of the locally randomly ordered spin-glass phase, the system orders globally as a nematic phase. This nematic ordering of the Heisenberg spin-glass system is dramatically different from the spin-glass ordering of the Ising spin-glass system. The system is solved exactly on a hierarchical lattice and, equivalently, Migdal-Kadanoff approximately on a cubic lattice. The global phase diagram is calculated, exhibiting this nematic phase, and ferromagnetic, antiferromagnetic, disordered phases. The nematic phase of the classical Heisenberg spin-glass system is also found in other dimensions $d>2$: We calculate nematic transition temperatures in 24 different dimensions in $2<d\le 4$.

Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and ${\mathrm{RP}}^2$ models. We demonstrate that uniform matrix product states (MPSs) with explicit $\mathrm{SO}\left(3\right)$ symmetry can probe correlation lengths up to $\mathrm{O}\left({10}^3\right)$ sites accurately, and we study the scaling of entanglement entropy and universal features of MPS entanglement spectra. For the Heisenberg model, we find no signs of a finite-temperature phase transition, supporting the scenario of asymptotic freedom. For the ${\mathrm{RP}}^2$ model we observe an abrupt onset of scaling behavior, consistent with hints of a finite-temperature phase transition reported in previous studies. A careful analysis of the softening of the correlation length divergence, the scaling of the entanglement entropy, and the MPS entanglement spectra shows that our results are inconsistent with true criticality, but are rather in agreement with the scenario of a crossover to a pseudocritical region which exhibits strong signatures of nematic quasi-long-range order at length scales below the true correlation length. Our results reveal a fundamental difference in scaling behavior between the Heisenberg and ${\mathrm{RP}}^2$ models: Whereas the emergence of scaling in the former shifts to zero temperature if the bond dimension is increased, it occurs at a finite bond-dimension independent crossover temperature in the latter.

Chemically active systems such as living cells are maintained out of thermal equilibrium due to chemical events which generate heat and lead to active fluctuations. A key question is to understand on which time and length scales active fluctuations dominate thermal fluctuations. Here, we formulate a stochastic field theory with Poisson white noise to describe the heat fluctuations which are generated by stochastic chemical events and lead to active temperature fluctuations. We find that on large length- and timescales, active fluctuations always dominate thermal fluctuations. However, at intermediate length- and timescales, multiple crossovers exist which highlight the different characteristics of active and thermal fluctuations. Our work provides a framework to characterize fluctuations in active systems and reveals that local equilibrium holds at certain length- and timescales.

We investigate the structure and activated dynamics of a binary mixture of colloidal particles dispersed in a solvent of much smaller-sized particles. The solvent degrees of freedom are traced out from the grand partition function of the colloid-solvent mixture which reduces the system from ternary to effective binary mixture of colloidal particles. In the effective binary mixture colloidal particles interact via effective potential that consists of bare potential plus the solvent-induced interaction. Expressions for the effective potentials and pair correlation functions are derived. We used the result of pair correlation functions to determine the number of particles in a cooperatively reorganizing cluster (CRC) in which localized particles form “long-lived” nonchemical bonds with the central particle. For an event of relaxation to take place these bonds have to reorganize irreversibly, the energy involved in the processes is the effective activation energy of relaxation. Results are reported for hard sphere colloidal particles dispersed in a solvent of hard sphere particles. Our results show that the concentration of solvent can be used as a control parameter to fine-tune the microscopic structural ordering and the size of CRC that governs the glassy dynamics. We show that a small variation in the concentration of solvent creates a bigger change in the kinetic fragility which highlights a wide variation in behavior, ranging from fragile to strong glasses. We conclude that the CRC which is determined from the static pair correlation function and the fluctuations embedded in the system is probably the sole player in the physics of glass transition.

Scanning tunneling microscopy experiments have revealed a spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyze an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimization of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analyzed, both analytically and numerically. All phases are characterized by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene.