In a recent paper [Phys. Rev. E 101, 050101(R) (2020)] an attempt is presented to formulate the nonequilibrium thermodynamics of an open system in terms of the Hamiltonian of mean force. The purpose of the present comment is to clarify severe restrictions of this approach and to stress that recently noted ambiguities [Phys. Rev. E 94, 022143 (2016)] of fluctuating thermodynamic potentials cannot be removed in the suggested way.

We refute the criticism expressed in a Comment by P. Talkner and P. Hänggi [Phys. Rev. E 102, 066101 (2020)] on our paper Phys. Rev. E 101, 050101(R) (2020). We first make clear that our paper is free of any technical mistakes. We then defend the statements of our paper which were claimed to be taken out of context. Finally, we give clear arguments showing that the basic concepts we rely on are meaningful and have a deep rational.

Recent work has introduced the term “procrystalline” to define systems which lack translational symmetry but have an underlying high-symmetry lattice. The properties of five such two-dimensional (2D) lattices are considered in terms of the topologies of rings which may be formed from three-coordinate sites only. Parent lattices with full coordination numbers of four, five, and six are considered, with configurations generated using a Monte Carlo algorithm. The different lattices are shown to generate configurations with varied ring distributions. The different constraints imposed by the underlying lattices are discussed. Ring size distributions are obtained analytically for two of the simpler lattices considered (the square and trihexagonal nets). In all cases, the ring size distributions are compared to those obtained via a maximum entropy method. The configurations are analyzed with respect to the near-universal Lemaître curve (which connects the fraction of six-membered rings with the width of the ring size distribution) and three lattices are highlighted as rare examples of systems which generate configurations which do not map onto this curve. The assortativities are considered, which contain information on the degree of ordering of different sized rings within a given distribution. All of the systems studied show systematically greater assortativities when compared to those generated using a standard bond-switching method. Comparison is also made to two series of crystalline motifs which shown distinctive behavior in terms of both the ring size distributions and the assortativities. Procrystalline lattices are therefore shown to have fundamentally different behavior to traditional disordered and crystalline systems, indicative of the partial ordering of the underlying lattices.

The stopping power of liquid water was measured for carbon ions with energies in the Bragg peak region using the inverted Doppler shift attenuation method. Among the semiempirical data, the results of this work agree best with the data recommended in the Errata and Addendum of ICRU Report No. 73, which is based on an $I$ value of 78 eV for water. The agreement was worse when the present results were compared to the newer recommendation of the ICRU published in ICRU Report No. 90. The srim code seems to slightly overestimate the stopping power of water for carbon ions above 3 MeV. A semiexperimental stopping power of water for α particles was derived from the present results using the theoretical ratio between the stopping powers of water for carbon ions and α particles computed by means of the casp code. These values agree well with the experimental data for α particles within the uncertainties.

Motivated by the one-drop-filling (ODF) method for the industrial manufacturing of liquid crystal displays, we analyze the pressure-driven flow of a nematic in a channel with dissipative weak planar anchoring at the boundaries of the channel. We obtain quasisteady asymptotic solutions for the director angle and the velocity in the limit of small Leslie angle, in which case the key parameters are the Ericksen number and the anchoring strength parameter. In the limit of large Ericksen number, the solution for the director angle has narrow reorientational boundary layers and a narrow reorientational internal layer separated by two outer regions in which the director is aligned at the positive Leslie angle in the lower half of the channel and the negative Leslie angle in the upper half of the channel. On the other hand, in the limit of small Ericksen number, the solution for the director angle is dominated by splay elastic effects with viscous effects appearing at first order. As the Ericksen number varies, there is a continuous transition between these asymptotic behaviors, and in fact the two asymptotic solutions capture the behavior rather well for all values of the Ericksen number. The steady-state value of the director angle at the boundaries and the timescale of the evolution toward this steady-state value in the asymptotic limits of large and small Ericksen number are determined. In particular, using estimated parameter values for the ODF method, it is found that the boundary director rotation timescale is substantially shorter than the timescale of the ODF method, suggesting that there is sufficient time for significant transient flow-driven distortion of the nematic molecules at the substrates from their required orientation to occur.

The standard model of classical density-functional theory (cDFT) for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated fundamental measure hard-sphere functionals suffer from potential numerical instabilities either due to possible instabilities in the functionals themselves or due to implementations that mix real- and Fourier-space components inconsistently. Here we present a new implementation based on a demonstrably stable hard-sphere functional that is implemented in a completely consistent manner. The present work does not depend on approximate spherical integration schemes and so is much more robust than previous algorithms. The methods are illustrated by calculating phase diagrams for the solid state using the standard Lennard-Jones potential as well as a new class of potentials recently proposed by Wang et al. [Phys. Chem. Chem. Phys. 22, 10624 (2020)]. The latter span the range from potentials for small molecules to those appropriate to colloidal systems simply by varying a parameter. We verify that cDFT is able to semiquantitatively reproduce the phase diagram in all cases. We also show that for these problems computationally cheap Gaussian approximations are nearly as good as full minimization based on finite differences.

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) is reexamined in the light of the recently introduced concept of global stability of the density functional based on its boundedness [Lutsko and Lam, Phys. Rev. E 98, 012604 (2018)]. It is shown that within the present paradigm, explicit stability of the functional can be achieved only at the cost of giving up accuracy at low densities. It is argued that this is an acceptable trade-off since the main value of DFT lies in the study of dense systems. Explicit calculations for a wide variety of systems show that a proposed explicitly stable functional is competitive in all ways with the popular White Bear models while sharing some of their weaknesses when applied to non-close-packed solids.

Kink-antikink scattering in nonintegrable field theories like ${\varphi }^4$ theory is still rather poorly understood beyond brute-force numerical calculations, even after several decades of investigation. Recently, however, some progress has been made based on the introduction of certain self-dual background fields in these field theories which imply both the existence of static kink-antikink solutions of the Bogomol'nyi type and the possibility of an adiabatic scattering (moduli space approximation). Here we continue and generalize these investigations by introducing a one-parameter family of models interpolating between the Bogomol'nyi-Prasad-Sommerfield (BPS) model with the self-dual background field and the original ${\varphi }^4$ theory. More concretely, we study kink-antikink scattering in a parameter range between the limit of no static force (BPS limit) and the regime where the static interaction between kink and antikink is small (non-BPS regime). This allows us to study the impact of the strength of the intersoliton static force on the soliton dynamics. In particular, we analyze how the transition of a bound mode through the mass threshold affects the soliton dynamics in a generic process, i.e., when a static intersoliton force shows up. We show that the thin, precisely localized spectral wall which forms in the limit of no static force broadens in a well-defined manner when a static force is included, giving rise to what we call a thick spectral wall. This phenomenon results from the appearance of a stationary saddle point solution where the acceleration of the solitons owing to the attractive force is compensated by the dynamics of the sufficiently excited mode. Thus, this barrier shows up before the mode crosses the mass threshold.

It is an established fact that a positive wave number plays an essential role in Turing instability. However, the impact of a negative wave number on Turing instability remains unclear. Here, we investigate the effect of the weights and nodes on Turing instability in the FitzHugh-Nagumo model, and theoretical results reveal genesis of Turing instability due to a negative wave number through the stability analysis and mean-field method. We obtain the Turing instability region in the continuous media system and provide the relationship between degree and eigenvalue of the network matrix by the Gershgorin circle theorem. Furthermore, the Turing instability condition about nodes and the weights is provided in the network-organized system. Additionally, we found chaotic behavior because of interactions between $I$ Turing instability and $II$ Turing instability. Besides, we apply this above analysis to explaining the mechanism of the signal conduction of the inhibitory neuron. We find a moderate coupling strength and corresponding number of links are necessary to the signal conduction.

Exact four-photon resonance of collinear planar laser pulses is known to be prohibited by the classical dispersion law of electromagnetic waves in plasma. We show here that the renormalization produced by an arbitrarily small relativistic electron nonlinearity removes this prohibition. The laser frequency shifts in collinear resonant four-photon scattering increase with laser intensities. For laser pulses of frequencies much greater than the electron plasma frequency, the shifts can also be much greater than the plasma frequency and even nearly double the input laser frequency at still small relativistic electron nonlinearities. This may enable broad range tunable lasers of very high frequencies and powers. Since the four-photon scattering does not rely on the Langmuir wave, which is very sensitive to plasma homogeneity, such lasers would also be able to operate at much larger plasma inhomogeneities than lasers based on stimulated Raman scattering in plasma.

K-shell x-ray spectra from Al wire hybrid X pinches have been studied using an x-ray streak camera with better than 0.1-ns time resolution together with a Focusing Spectrograph with Spatial Resolution (FSSR) spectrograph. High-intensity radiation with a continuumlike spectrum was observed in the subnanosecond initial phase of the x-ray pulse generated by the hybrid X pinch (HXP). The absence of spectral lines in this phase and the extremely small x-ray source size indicates the importance of radiative processes in the final phase implosion dynamics. Plasma parameters in the following phases of the HXP were determined from analysis of the line intensities. Point-projection radiography together with a slit-step wedge camera and an FSSR spectrograph without time resolution were used to show the number of radiation sources, and to give information on the time-integrated photon energy spectrum.

We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle-number conservation $\left[U\right(1\left)\right]$ symmetry. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless time which scales with the size $L$ as $\mathcal{O}\left(L^2\right)$, or $\mathcal{O}\left(L^0\right)$, in the presence, or absence, of $U\left(1\right)$ symmetry, respectively. Using a random phase assumption which essentially requires a long-range nature of the interaction, we demonstrate that the Thouless time scaling is equivalent to the behavior of the spectral gap of a classical Markov chain, which is in the continuous-time (Trotter) limit generated, respectively, by a gapless $XXX$, or gapped $XXZ$, spin-1/2 chain Hamiltonian.

When a quantum system is subject to a thermal gradient it may sustain a steady nonequilibrium heat current by entering into a so-called nonequilibrium steady state (NESS). Here we show that NESS constitute a thermodynamic resource that can be exploited to charge a quantum battery. This adds to the list of recently reported sources available at the nanoscale, such as coherence, entanglement, and quantum measurements. We elucidate this concept by showing analytic and numerical studies of a two-qubit quantum battery that is alternatively charged by an incoherent heat flow and discharged by application of a properly chosen unitary gate. The presence of a NESS for the charging step guarantees steady operation with positive power output. Decreasing the duration of the charging step results in a time-periodic steady state accompanied by increased efficiency and output power. The device is amenable to implementation with different nanotechnology platforms.

The stochastic Liouville–von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

All local bond-state densities are calculated for $q$-state Potts and clock models in three spatial dimensions, $d=3$. The calculations are done by an exact renormalization group on a hierarchical lattice, including the density recursion relations, and simultaneously are the Migdal-Kadanoff approximation for the cubic lattice. Reentrant behavior is found in the interface densities under symmetry breaking, in the sense that upon lowering the temperature, the value of the density first increases and then decreases to its zero value at zero temperature. For this behavior, a physical mechanism is proposed. A contrast between the phase transition of the two models is found and explained by alignment and entropy, as the number of states $q$ goes to infinity. For the clock models, the renormalization-group flows of up to 20 energies are used.

Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent approach for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but potentially inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on the community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between the connectivity patterns in different layers. Finally, we explain how to use correlated models for edge “prediction” (i.e., inference) in multilayer networks. By incorporating edge correlations, we find that prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously purchased grocery products.

We propose a mechanism to generate a single intense circularly polarized attosecond x-ray pulse from the interaction of a circularly polarized relativistic few-cycle laser pulse with an ultrathin foil at normal incidence. Analytical modeling and particle-in-cell simulation demonstrate that a huge charge-separation field can be produced when all the electrons are displaced from the target by the incident laser, resulting in a high-quality relativistic electron mirror that propagates against the tail of the laser pulse. The latter is efficiently reflected as well as compressed into an attosecond pulse that is also circularly polarized.

We investigate a model of magnetic friction with the infinite-range interaction by mean-field analysis and a numerical simulation, and compare its behavior with that of the short-range model that we considered previously [Komatsu, Phys. Rev. E 100, 052130 (2019)]. This infinite-range model always obeys the Stokes law when the temperature is higher than the critical value, $T_c$, whereas it shows a crossover or transition from the Dieterich-Ruina law to the Stokes law when the temperature is lower than $T_c$. Considering that the short-range model in our previous study shows a crossover or transition irrespective of whether the temperature is above or below the equilibrium transition temperature, the behavior in the high-temperature state is the major difference between these two models.

The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano-Sasa entropy production. Notably, the obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.