The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics.

The Boltzmann equation framework for inelastic Maxwell models is considered to determine the transport coefficients associated with the mass, momentum, and heat fluxes of a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. The Boltzmann equation is solved by means of a Chapman-Enskog–type expansion around the (local) shear flow distributions $f_r^{\left(0\right)}$ for each species that retain all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the transport processes instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled equations, which can be analytically solved as functions of the shear rate $a$, the coefficients of restitution ${\alpha }_{rs}$, and the parameters of the mixture (masses, diameters, and composition). Since the reference distribution functions $f_r^{\left(0\right)}$ apply for arbitrary values of the shear rate and are not restricted to weak dissipation, the corresponding generalized coefficients turn out to be nonlinear functions of both $a$ and ${\alpha }_{rs}$. The dependence of the relevant elements of the three diffusion tensors on both the shear rate and dissipation is illustrated in the tracer limit case, the results showing that the deviation of the generalized transport coefficients from their forms for vanishing shear rates is in general significant. A comparison with the previous results obtained analytically for inelastic hard spheres by using Grad's moment method is carried out, showing a good agreement over a wide range of values for the coefficients of restitution. Finally, as an application of the theoretical expressions derived here for the transport coefficients, thermal diffusion segregation of an intruder immersed in a granular gas is also studied.

We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium low-temperature classical phase simultaneously breaks continuous translational symmetry and dynamic space-time homogeneity, whose absence is usually associated with out-of-equilibrium glassy phenomena. This results in an exotic self-assembled cluster crystal with coexisting liquidlike long-time dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on cluster-glassy crystals are separate and competing: Zero-point motion tends to destabilize crystalline order, which can be restored by bosonic statistics.

We explore the link between soft vibrational modes and local relaxation events in polymer glasses during physical aging, active deformation at constant strain rate, and subsequent recovery. A softness field is constructed out of the superposition of the amplitudes of the lowest energy normal modes, and found to predict up to 70% of the rearrangements. Overlap between softness and rearrangements increases logarithmically during aging and recovery phases as energy barriers rise due to physical aging, while yielding rapidly rejuvenates the overlap to that of a freshly prepared glass. In the strain hardening regime, correlations rise for uniaxial tensile deformation but not for simple shear. These trends can be explained by considering the differing degrees of localization of the soft modes in the two deformation protocols.

Bacterial light-harvesting pigment-protein complexes are very efficient at converting photons into excitons and transferring them to reaction centers, where the energy is stored in a chemical form. Optical properties of the complexes are known to change significantly in time and also vary from one complex to another; therefore, a detailed understanding of the variations on the level of single complexes and how they accumulate into effects that can be seen on the macroscopic scale is required. While experimental and theoretical methods exist to study the spectral properties of light-harvesting complexes on both individual complex and bulk ensemble levels, they have been developed largely independently of each other. To fill this gap, we simultaneously analyze experimental low-temperature single-complex and bulk ensemble optical spectra of the light-harvesting complex-2 (LH2) chromoproteins from the photosynthetic bacterium Rhodopseudomonas acidophila in order to find a unique theoretical model consistent with both experimental situations. The model, which satisfies most of the observations, combines strong exciton-phonon coupling with significant disorder, characteristic of the proteins. We establish a detailed disorder model that, in addition to containing a $C_2$-symmetrical modulation of the site energies, distinguishes between static intercomplex and slow conformational intracomplex disorders. The model evaluations also verify that, despite best efforts, the single-LH2-complex measurements performed so far may be biased toward complexes with higher Huang-Rhys factors.

Information maximization has been investigated as a possible mechanism of learning governing the self-organization that occurs within the neural systems of animals. Within the general context of models of neural systems bidirectionally interacting with environments, however, the role of information maximization remains to be elucidated. For bidirectionally interacting physical systems, universal laws describing the fluctuation they exhibit and the information they possess have recently been discovered. These laws are termed fluctuation theorems. In the present study, we formulate a theory of learning in neural networks bidirectionally interacting with environments based on the principle of information maximization. Our formulation begins with the introduction of a generalized fluctuation theorem, employing an interpretation appropriate for the present application, which differs from the original thermodynamic interpretation. We analytically and numerically demonstrate that the learning mechanism presented in our theory allows neural networks to efficiently explore their environments and optimally encode information about them.

We present a previously unrecognized effect of sound waves on gap-junction-based intercellular signaling such as in biological tissues composed of endothelial cells. We suggest that sound irradiation may, through temporal and spatial modulation of cell-to-cell conductance, create intercellular calcium waves with unidirectional signal propagation associated with nonconventional topologies. Nonreciprocity in calcium wave propagation induced by sound wave irradiation is demonstrated in the case of a linear and a nonlinear reaction-diffusion model. This demonstration should be applicable to other types of gap-junction-based intercellular signals, and it is thought that it should be of help in interpreting a broad range of biological phenomena associated with the beneficial therapeutic effects of sound irradiation and possibly the harmful effects of sound waves on health.

For many physical systems at any given temperature, the set of all states where the system's free energy reaches its largest value can be determined from the system's constitutive equations of internal energy and entropy, once a state of that set is known. Such an approach is fraught with complications when applied to a living cell, because the cell's cytosol contains thousands of solutes, and thus thousands of state variables, which makes determination of its state impractical. We show here that, when looking for the maximum energy that the cytosol can store and release, detailed information on cytosol composition is redundant. Compatibility with cell's life requires that a single variable that represents the overall concentration of cytosol solutes must fall between defined limits, which can be determined by dehydrating and overhydrating the cell to its maximum capacity. The same limits are shown to determine, in particular, the maximum amount of free energy that a cell can supply in fast anaerobic processes, starting from any given initial state. For a typical skeletal muscle in normal physiological conditions this energy, i.e., the maximum anaerobic capacity to do work, is calculated to be about 960 J per kg of muscular mass. Such energy decreases as the overall concentration of solutes in the cytosol is increased. Similar results apply to any kind of cell. They provide an essential tool to understand and control the macroscopic response of single cells and multicellular cellular tissues alike. The applications include sport physiology, cell aging, disease produced cell damage, drug absorption capacity, to mention the most obvious ones.

For numerical simulations of crowd dynamics in an evacuation we need a computationally light environment, such as the cellular automaton model (CA). By choosing the right model parameters, different types of crowd behavior and collective effects can be produced. But the CA does not answer why, when, and how these different behaviors and collective effects occur. In this article, we present a model, where we couple a spatial evacuation game to the CA. In the game, an agent chooses its strategy by observing its neighbors' strategies. The game matrix changes with the distance to the exit as the evacuation conditions develop. In the resulting model, an agent's strategy choice alters the parameters that govern its behavior in the CA. Thus, with our model, we are able to simulate how evacuation conditions affect the behavior of the crowd. Also, we show that some of the collective effects observed in evacuations are a result of the simple game the agents play.

We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ${\hslash }_{\mathrm{eff}}$ values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results—obtained for the mean currents and asymptotic distributions only—and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.

The nonmodal linear stability of miscible viscous fingering in a two-dimensional homogeneous porous medium has been investigated. The linearized perturbed equations for Darcy's law coupled with a convection-diffusion equation is discretized using a finite difference method. The resultant initial value problem is solved by a fourth-order Runge-Kutta method, followed by a singular value decomposition of the propagator matrix. Particular attention is given to the transient behavior rather than the long-time behavior of eigenmodes predicted by the traditional modal analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the $\epsilon$-pseudospectra structures and the largest energy growth function, respectively. With the help of nonmodal stability analysis we demonstrate that at early times the displacement flow is dominated by diffusion and the perturbations decay. At later times, when convection dominates diffusion, perturbations grow. Furthermore, we show that the dominant perturbation that experiences the maximum amplification within the linear regime lead to the transient growth. These two important features were previously unattainable in the existing linear stability methods for miscible viscous fingering. To explore the relevance of the optimal perturbation obtained from nonmodal analysis, we performed direct numerical simulations using a highly accurate pseudospectral method. Furthermore, a comparison of the present stability analysis with existing modal and initial value approach is also presented. It is shown that the nonmodal stability results are in better agreement than the other existing stability analyses, with those obtained from direct numerical simulations.

We demonstrate that chemical reactions leading to the formation of AlO radicals in plasmas produced by ablation of aluminum or Ti-sapphire with ultraviolet nanosecond laser pulses can be predicted by the model of local thermodynamic equilibrium. Therefore, emission spectra recorded with an echelle spectrometer and a gated detector were compared to the spectral radiance computed for uniform and nonuniform equilibrium plasmas. The calculations are based on analytical solutions of the radiation transfer equation. The simulations show that the plasmas produced in argon background gas are almost uniform, whereas temperature and density gradients are evidenced in air. Furthermore, chemical reactions exclusively occur in the cold plume periphery for ablation in air. The formation of AlO is negligible in argon as the plasma temperature is too large in the time interval of interest up to several microseconds. Finally, the validity of local thermodynamic equilibrium is shown to depend on time, space, and on the elemental composition. The presented conclusions are of interest for material analysis via laser-induced breakdown spectroscopy and for laser materials processing.

The ablator material for inertial confinement fusion (ICF) capsules on the Laser Mégajoule is a glow-discharge polymer (GDP) plastic. Its equation of state (EOS) is of primary importance for the design of such capsules, since it has direct consequences on shock timing and is essential to mitigate hydrodynamic instabilities. Using ab initio molecular dynamics (AIMD), we have investigated the 300-K isotherm of amorphous ${\mathrm{CH}}_{1.37}{\mathrm{O}}_{0.08}$ plastic, whose structure is close to GDP plastic. The 300-K isotherm, which is often used as a cold curve within tabular EOS, is an important contribution of the EOS in the multimegabar pressure range. AIMD results are compared to analytic models within tabular EOS, pointing out large discrepancies. In addition, we show that the effect of oxygen decreases 300-K isotherm pressure by 10%–15%. The implication of these observations is the ability to improve ICF target performance, which is essential to achieve fusion ignition.

The interaction of a strong flux of photons with matter through an ionizing front (I-front) is an ubiquitous phenomenon in the context of astrophysics and inertial confinement fusion (ICF) where intense sources of radiation put matter into motion. When the opacity of the irradiated material varies continuously in the radiation spectral domain, only one single I-front is formed. In contrast, as numerical simulations tend to show, when the opacity of the irradiated material presents a sharp edge in the radiation spectral domain, a second I-front (an edge front) can form. A full description of the mechanism behind the formation of this edge front is presented in this article. It allows us to understand extra shocks (edge-shocks), displayed by ICF simulations, that might affect the robustness of the design of fusion capsules in actual experiments. Moreover, it may have consequences in various domains of astrophysics where ablative flows occur.

We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system may be realized in nonlinear optics and Bose-Einstein condensates. By means of a similarity transformation, we establish a connection between solutions of the coupled Manakov system with spatially variable coefficients and the basic Manakov model with constant coefficients. Exact solutions in the form of two-component Peregrine and dromion waves are obtained. The RW dynamics is analyzed for different choices of parameters in the underlying parameter space. Different classes of RW solutions are categorized by means of a naturally introduced control parameter which takes integer values.

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD “training” data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD “test” data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.

We present time-resolved observations of Rayleigh-Taylor-instability (RTI) evolution at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time $\left(\sim 10\mu \mathrm{s}\right)$ is consistent with the estimated linear RTI growth rate calculated using experimentally inferred values of density $\left(\sim {10}^{14}{\mathrm{cm}}^{-3}\right)$ and deceleration $(\sim {10}^9$ $m/{\mathrm{s}}^2)$. The observed mode wavelength $(\gtrsim 1$ cm) nearly doubles within a linear growth time. Theoretical estimates of magnetic and viscous stabilization and idealized magnetohydrodynamic simulations including a physical viscosity model both suggest that the observed instability evolution is subject to magnetic and/or viscous effects.

We propose a method to identify the order of a quantum phase transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the quantum cusp and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.

We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena.