The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying microcanonical thermostatistics. Here we provide a detailed comparison of the most commonly considered microcanonical entropy definitions, focusing specifically on whether they satisfy or violate the zeroth, first, and second laws of thermodynamics. Our analysis shows that, for a broad class of systems that includes all standard classical Hamiltonian systems, only the Gibbs volume entropy fulfills all three laws simultaneously. To avoid ambiguities, the discussion is restricted to exact results and analytically tractable examples.

The statistical mechanics of a one-dimensional Ising model in thermal equilibrium is well-established, textbook material. Yet, when driven far from equilibrium by coupling two sectors to two baths at different temperatures, it exhibits remarkable phenomena, including an unexpected “freezing by heating.” These phenomena are explored through systematic numerical simulations. Our study reveals complicated relaxation processes as well as a crossover between two very different steady-state regimes.

Colloidal glasses, bird feathers, and beetle scales can all show structural colors arising from short-ranged spatial correlations between scattering centers. Unlike the structural colors arising from Bragg diffraction in ordered materials like opals, the colors of these photonic glasses are independent of orientation, owing to their disordered, isotropic microstructures. However, there are few examples of photonic glasses with angle-independent red colors in nature, and colloidal glasses with particle sizes chosen to yield structural colors in the red show weak color saturation. Using scattering theory, we show that the absence of angle-independent red color can be explained by the tendency of individual particles to backscatter light more strongly in the blue. We discuss how the backscattering resonances of individual particles arise from cavity-like modes and how they interact with the structural resonances to prevent red. Finally, we use the model to develop design rules for colloidal glasses with red, angle-independent structural colors.

Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems and characterized in the laboratory as showing unusual phase relationships in population dynamics, including a $\pi$ phase shift between predator and prey (evolutionary cycles) and even undetectable prey oscillations compared to those of the predator (cryptic cycles). Here we present a generic individual-level stochastic model of interacting populations that includes a subpopulation of low nutritional value to the predator. Using a master equation formalism and by mapping to a coherent state path integral solved by a system-size expansion, we show that evolutionary and cryptic quasicycles can emerge generically from the combination of intrinsic demographic fluctuations and clonal mutations alone, without additional biological mechanisms.

We present results from direct, large-scale molecular dynamics simulations of homogeneous bubble (liquid-to-vapor) nucleation. The simulations contain half a billion Lennard-Jones atoms and cover up to 56 million time steps. The unprecedented size of the simulated volumes allows us to resolve the nucleation and growth of many bubbles per run in simple direct micro-canonical simulations while the ambient pressure and temperature remain almost perfectly constant. We find bubble nucleation rates which are lower than in most of the previous, smaller simulations. It is widely believed that classical nucleation theory (CNT) generally underestimates bubble nucleation rates by very large factors. However, our measured rates are within two orders of magnitude of CNT predictions; only at very low temperatures does CNT underestimate the nucleation rate significantly. Introducing a small, positive Tolman length leads to very good agreement at all temperatures, as found in our recent vapor-to-liquid nucleation simulations. The critical bubbles sizes derived with the nucleation theorem agree well with the CNT predictions at all temperatures. Local hot spots reported in the literature are not seen: Regions where a bubble nucleation event will occur are not above the average temperature, and no correlation of temperature fluctuations with subsequent bubble formation is seen.

We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble, that the system (i) obeys a barometric formula for the density profile, and (ii) the kinetic temperature is independent of height, even when the system is small. We show here that in the microcanonical ensemble the kinetic temperature of the particles affected by the field is not constant with height, but that rather, generally speaking, it decreases with a gradient of order $1/N$. Even more, if we have a mixture of two species, one which is influenced by the field and the other which is not, we find that the two species' kinetic temperatures are generally different, even at the same height. These facts are shown in detail by studying a simple mechanical model: a Lorentz Gas where particles and spinning disks interact and the particles are subjected to a constant external force. In the microcanonical ensemble, the kinetic temperature of the particles is indeed found to vary with height; the disks' kinetic temperature, on the other hand, is height-independent, and thus, differs from that of the particles with which they interact.

We describe a simple model of heterogeneous, interacting agents making decisions between $n\ge 2$ discrete choices. For a special class of interactions, our model is the mean field description of random field Potts-like models and is effectively solved by finding the extrema of the average energy $E$ per agent. In these cases, by studying the propagation of decision changes via avalanches, we argue that macroscopic dynamics is well captured by a gradient flow along $E$. We focus on the permutation symmetric case, where all $n$ choices are (on average) the same, and spontaneous symmetry breaking (SSB) arises purely from cooperative social interactions. As examples, we show that bimodal heterogeneity naturally provides a mechanism for the spontaneous formation of hierarchies between decisions and that SSB is a preferred instability to discontinuous phase transitions between two symmetric points. Beyond the mean field limit, exponentially many stable equilibria emerge when we place this model on a graph of finite mean degree. We conclude with speculation on decision making with persistent collective oscillations. Throughout the paper, we emphasize analogies between methods of solution to our model and common intuition from diverse areas of physics, including statistical physics and electromagnetism.

Malaria is transmitted to vertebrates via a mosquito bite, during which rodlike and crescent-shaped parasites, called sporozoites, are injected into the skin of the host. Searching for a blood capillary to penetrate, sporozoites move quickly in locally helical trajectories, that are frequently perturbed by interactions with the extracellular environment. Here we present a theoretical analysis of the active motility of sporozoites in a structured environment. The sporozoite is modelled as a self-propelled rod with spontaneous curvature and bending rigidity. It interacts with hard obstacles through collision rules inferred from experimental observation of two-dimensional sporozoite movement in pillar arrays. Our model shows that complex motion patterns arise from the geometrical shape of the parasite and that its mechanical flexibility is crucial for stable migration patterns. Extending the model to three dimensions reveals that a bent and twisted rod can associate to cylindrical obstacles in a manner reminiscent of the association of sporozoites to blood capillaries, supporting the notion of a prominent role of cell shape during malaria transmission.

Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks, little work has been devoted to the understanding of how such heterogeneities can emerge from microscopic mechanisms at the level of nodes and links. Here we show that long-term memory effects are present in the creation and disappearance of links in empirical networks. We thus consider a simple generative modeling framework for temporal networks able to incorporate these memory mechanisms. This allows us to study separately the role of each of these mechanisms in the emergence of heterogeneous network dynamics. In particular, we show analytically and numerically how heterogeneous distributions of contact durations, of intercontact durations, and of numbers of contacts per link emerge. We also study the individual effect of heterogeneities on dynamical processes, such as the paradigmatic susceptible-infected epidemic spreading model. Our results confirm in particular the crucial role of the distributions of intercontact durations and of the numbers of contacts per link.

Plants create sugar in the mesophyll cells of their leaves by photosynthesis. This sugar, mostly sucrose, has to be loaded via the bundle sheath into the phloem vascular system (the sieve elements), where it is distributed to growing parts of the plant. We analyze the feasibility of a particular loading mechanism, active symplasmic loading, also called the polymer trap mechanism, where sucrose is transformed into heavier sugars, such as raffinose and stachyose, in the intermediary-type companion cells bordering the sieve elements in the minor veins of the phloem. Keeping the heavier sugars from diffusing back requires that the plasmodesmata connecting the bundle sheath with the intermediary cell act as extremely precise filters, which are able to distinguish between molecules that differ by less than 20% in size. In our modeling, we take into account the coupled water and sugar movement across the relevant interfaces, without explicitly considering the chemical reactions transforming the sucrose into the heavier sugars. Based on the available data for plasmodesmata geometry, sugar concentrations, and flux rates, we conclude that this mechanism can in principle function, but that it requires pores of molecular sizes. Comparing with the somewhat uncertain experimental values for sugar export rates, we expect the pores to be only 5%–10% larger than the hydraulic radius of the sucrose molecules. We find that the water flow through the plasmodesmata, which has not been quantified before, contributes only 10%–20% to the sucrose flux into the intermediary cells, while the main part is transported by diffusion. On the other hand, the subsequent sugar translocation into the sieve elements would very likely be carried predominantly by bulk water flow through the plasmodesmata. Thus, in contrast to apoplasmic loaders, all the necessary water for phloem translocation would be supplied in this way with no need for additional water uptake across the plasma membranes of the phloem.

Two colloidal particles, driven around an optical vortex trap, have been recently shown to pair due to an interplay between hydrodynamic interactions and the curved path they are forced to follow. We demonstrate here that this pairing interaction can be tuned experimentally, and we study its effect on the collective excitations of many particles driven around such an optical trap. We find that even though the system is overdamped, hydrodynamic interactions due to driving give rise to nondecaying excitations with characteristic dispersion relations. The collective excitations of the colloidal ring reflect fluctuations of particle pairs rather than those of single particles.

In this work we study the effect of behavioral changes of individuals on the propagation of epidemic diseases. Specifically, we consider a susceptible-infected-susceptible model over a network of contacts that evolves in a time scale that is comparable to the individual disease dynamics. The phenomenon is modeled in the context of activity-driven networks, in which contacts occur on the basis of activity potentials. To offer insight into behavioral strategies targeting both susceptible and infected individuals, we consider two separate behaviors that may emerge in respiratory syndromes and sexually transmitted infections. The first is related to a reduction in the activity of infected individuals due to quarantine or illness. The second is instead associated with a selfish self-protective behavior of susceptible individuals, who tend to reduce contact with the rest of the population on the basis of a risk perception. Numerical and theoretical results suggest that behavioral changes could have a beneficial effect on the disease spreading, by increasing the epidemic threshold and decreasing the steady-state fraction of infected individuals.

Experiments suggest that the migration of some cells in the three-dimensional extracellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell made of two beads and an active spring moving along a rigid track. The active spring models the stress fibers with their myosin-driven contractility and $\alpha$-actinin-driven extendability, while the friction coefficients of the two beads describe the catch and slip-bond behaviors of the integrins in focal adhesions. In the absence of active noise, net motion arises from an interplay between active contractility (and passive extendability) of the stress fibers and an asymmetry between the front and back of the cell due to catch-bond behavior of integrins at the front of the cell and slip-bond behavior of integrins at the back. We obtain reasonable cell speeds with independently estimated parameters. We also study the effects of hysteresis in the active spring, due to catch-bond behavior and the dynamics of cross linking, and the addition of active noise on the motion of the cell. Our model highlights the role of $\alpha$-actinin in three-dimensional cell motility and does not require Arp2/3 actin filament nucleation for net motion.

We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles exert an excess pressure on the interface and also move along the interface while the swimming direction changes due to rotational diffusion. We study the intricate influence of these self-propelled insoluble surfactants on the stability of the film surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of the in-surface swimming velocity, several characteristic instability modes can occur. In particular, rotational diffusion can either stabilize the film or induce instabilities of different character.

We developed a heuristic method for determining the ground-state degeneracy of hydrophobic-polar (HP) lattice proteins, based on Wang-Landau and multicanonical sampling. It is applied during comprehensive studies of single-site mutations in specific HP proteins with different sequences. The effects in which we are interested include structural changes in ground states, changes of ground-state energy, degeneracy, and thermodynamic properties of the system. With respect to mutations, both extremely sensitive and insensitive positions in the HP sequence have been found. That is, ground-state energies and degeneracies, as well as other thermodynamic and structural quantities, may be either largely unaffected or may change significantly due to mutation.

We study the evolution and failure of a granular slope as a function of prepared volume fraction, ${\varphi }_0$. We rotated an initially horizontal layer of granular material (0.3-mm-diam glass spheres) to a ${45}^{\circ }$ angle while we monitor the motion of grains from the side and top with high-speed video cameras. The dynamics of grain motion during the tilt process depended sensitively on ${\varphi }_0\in [0.58–0.63]$ and differed above or below the granular critical state, ${\varphi }_c$, defined as the onset of dilation as a function of increasing volume fraction. For ${\varphi }_0-{\varphi }_c<0$, slopes experienced short, rapid, precursor compaction events prior to the onset of a sustained avalanche. Precursor compaction events began at an initial angle ${\theta }_0=7.7\pm 1.4^{\circ }$ and occurred intermittently prior to the onset of an avalanche. Avalanches occurred at the maximal slope angle ${\theta }_m=28.5\pm 1.0^{\circ }$. Granular material at ${\varphi }_0-{\varphi }_c>0$ did not experience precursor compaction prior to avalanche flow, and instead experienced a single dilational motion at ${\theta }_0=32.1\pm 1.5^{\circ }$ prior to the onset of an avalanche at ${\theta }_m=35.9\pm 0.7^{\circ }$. Both ${\theta }_0$ and ${\theta }_m$ increased with ${\varphi }_0$ and approached the same value in the limit of random close packing. The angle at which avalanching grains came to rest, ${\theta }_R=22\pm 2^{\circ }$, was independent of ${\varphi }_0$. From side-view high-speed video, we measured the velocity field of intermittent and avalanching flow. We found that flow direction, depth, and duration were affected by ${\varphi }_0$, with ${\varphi }_0-{\varphi }_c<0$ precursor flow extending deeper into the granular bed and occurring more rapidly than precursor flow at ${\varphi }_0-{\varphi }_c>0$. Our study elucidates how initial conditions—including volume fraction—are important determinants of granular slope stability and the onset of avalanches.

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.

Let a lattice gas of constant density, described by the symmetric simple exclusion process, be brought in contact with a “target”: a spherical absorber of radius $R$. Employing the macroscopic fluctuation theory (MFT), we evaluate the probability $\mathcal{P}\left(T\right)$ that no gas particle hits the target until a long but finite time $T$. We also find the most likely gas density history conditional on the nonhitting. The results depend on the dimension of space $d$ and on the rescaled parameter $\ell =R/\sqrt{D_{0}T}$, where $D_0$ is the gas diffusivity. For small $\ell$ and $d>2$, $\mathcal{P}\left(T\right)$ is determined by an exact stationary solution of the MFT equations that we find. For large $\ell$, and for any $\ell$ in one dimension, the relevant MFT solutions are nonstationary. In this case, $ln\mathcal{P}\left(T\right)$ scales differently with relevant parameters, and it also depends on whether the initial condition is random or deterministic. The latter effects also occur if the lattice gas is composed of noninteracting random walkers. Finally, we extend the formalism to a whole class of diffusive gases of interacting particles.

We determine experimentally the angle $\alpha$ of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity $U$ for Bond numbers ${\mathrm{Bo}}_D=D/{\lambda }_c$ ranging between 0.1 and 4.2, where $D$ is the cylinder diameter and ${\lambda }_c$ the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, $\alpha \sim U^{-1}$, but with different prefactors depending on the value of ${\mathrm{Bo}}_D$. For small ${\mathrm{Bo}}_D$ (large capillary effects), the wake angle approximately follows the law $\alpha \simeq c_{\mathrm{g},\min }/U$, where $c_{\mathrm{g},\min }$ is the minimum group velocity of capillary-gravity waves. For larger ${\mathrm{Bo}}_D$ (weak capillary effects), we recover a law $\alpha \sim \sqrt{gD}/U$ similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. 110, 214503 (2013)]. Using the general property of dispersive waves that the characteristic wavelength of the wave packet emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law $\alpha \simeq c_{\mathrm{g},\min }/U$ originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.

When they reach a flat plain, rivers often deposit their sediment load into a cone-shaped structure called alluvial fan. We present a simplified experimental setup that reproduces, in one dimension, basic features of alluvial fans. A mixture of water and glycerol transports and deposits glass beads between two transparent panels separated by a narrow gap. As the beads, which mimic natural sediments, get deposited in this gap, they form an almost one-dimensional fan. At a moderate sediment discharge, the fan grows quasistatically and maintains its slope just above the threshold for sediment transport. The water discharge determines this critical slope. At leading order, the sediment discharge only controls the velocity at which the fan grows. A more detailed analysis reveals a slight curvature of the fan profile, which relates directly to the rate at which sediments are transported.