Consciousness is supported by complex patterns of brain activity which are indicative of irreversible nonequilibrium dynamics. While the framework of stochastic thermodynamics has facilitated the understanding of physical systems of this kind, its application to infer the level of consciousness from empirical data remains elusive. We faced this challenge by calculating entropy production in a multivariate Ornstein-Uhlenbeck process fitted to Functional magnetic resonance imaging brain activity recordings. To test this approach, we focused on the transition from wakefulness to deep sleep, revealing a monotonous relationship between entropy production and the level of consciousness. Our results constitute robust signatures of consciousness while also advancing our understanding of the link between consciousness and complexity from the fundamental perspective of statistical physics.

We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than the periodicity of the potential, the packet of spreading particles, all starting from a common origin, converges to a normal distribution centered at the origin with a mean-squared displacement that grows as $2D^{*}t$, with an effective diffusion constant that is smaller than that of a freely diffusing particle. We examine the interplay between this coarse-grained description and the fine structure of the density, which is given by the Boltzmann-Gibbs (BG) factor $e^{-V\left(x\right)/k_{B}T}$, the latter being nonnormalizable. We explain this result and construct a theory of observables using the Fokker-Planck equation. These observables are classified as those that are related to the BG fine structure, like the energy or occupation times, while others, like the positional moments, for long times, converge to those of the large-scale description. Entropy falls into a special category as it has a coarse-grained and a fine structure description. The basic thermodynamic formula $F=TS-E$ is extended to this far-from-equilibrium system. The ergodic properties are also studied using tools from infinite ergodic theory.

One of the Darken equations gives a relationship between the intrinsic and the tracer diffusion coefficients, $D_A$ and $D_A^{*}$, of species $A$ in a solid binary mixture. In its original formulation, the equation reads $D_A=D_A^{*}\mathrm{\Gamma }$, with $\mathrm{\Gamma }$ the thermodynamic factor. The question addressed in this paper is how $D_A$ and $D_A^{*}$ depend separately on $\mathrm{\Gamma }$. Using a recent result for transition probabilities in terms of the excess chemical potential [M. Di Muro and M. Hoyuelos, Phys. Rev. E 104, 044104 (2021)], it is shown that the intrinsic diffusivity does not depend on $\mathrm{\Gamma }$. This approach simplifies a previous theoretical analysis that reaches the same result. Experimental results of diffusion in Ni-Pd and Fe-Pd alloys [M. J. H. van Dal et al., Acta Mater. 48, 385 (2000)] are used to check the theory. Numerical simulations of Ni-Pd were performed to show that the migration energy is the main factor responsible for the increase in diffusivity at intermediate concentrations.

A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax toward an equilibrium. It is found that quantum coherence of the initial product states in the energy eigenbasis of the subsystems—quantified by the off-diagonal elements of the subsystem density matrices—can be viewed as a resource for equilibration and thermalization as manifested by the entanglement generated. Results are given for four distinct perturbation strength regimes, the ultraweak, weak, intermediate, and strong regimes. For each, three types of tensor product states are considered for the initial state: uniform superpositions, random superpositions, and individual subsystem eigenstates. A universal timescale is identified involving the interaction strength parameter. In particular, maximally coherent initial product states (a form of uniform superpositions) thermalize under time evolution for any perturbation strength in spite of the fact that in the ultraweak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like; though the time taken to thermalize tends to infinity as the interaction vanishes. Moreover, it is shown that in the ultraweak regime the initial entanglement growth of the system whose initial states are maximally coherent is quadratic-in-time, in contrast to the widely observed linear behavior.

In this paper, we present a self-consistent field theory of macroscopic forces in spatially inhomogeneous flexible chain polyelectrolyte solutions. We derive an analytical expression for a stress tensor which consists of three terms: isotropic hydrostatic stress, electrostatic (Maxwell) stress, and stress rising from conformational entropy of polymer chains—conformational stress. We apply our theory to the description of polyelectrolyte solutions confined in a conductive slit nanopore and observe anomalous behavior of disjoining pressure and electric differential capacitance.

Knowing if an optimal solution is local or global has always been a hard question to answer in more sophisticated situations of optimization problems. In this paper, for finite-time and weak isothermal driving processes, we show the existence of a global optimal protocol for the entropy production. We prove this by showing its convexity as a functional in the derivative of the protocol. This property also proves its monotonicity in such a context, which leads to the satisfaction of the second law of thermodynamics. In the end, we exemplify that the analytical technique of the Euler-Lagrange equation applied to overdamped Brownian motion delivers the global optimal protocol, by comparing it with the results of the global optimization technique of genetic programming.

Quorum sensing (QS) allows bacterial cells to sense changes in local cell density and, hence, to regulate multicellular processes, including biofilm formation, regulation of virulence, and horizontal gene transfer. While, traditionally, QS was thought to involve the exchange of extracellular signal molecules free in solution, recent experiments have shown that for some bacterial systems a substantial fraction of signal molecules are packaged and delivered in extracellular vesicles. How the packaging of signal molecules in extracellular vesicles influences the ability of cells to communicate and coordinate multicellular behaviors remains largely unknown. We present here a stochastic reaction-diffusion model of QS that accounts for the exchange of both freely diffusing and vesicle-associated signal molecules. We find that the delivery of signal molecules via extracellular vesicles amplifies local fluctuations in the signal concentration, which can strongly affect the dynamics and spatial range of bacterial communication. For systems with multiple bacterial colonies, extracellular vesicles provide an alternate pathway for signal transport between colonies, and may be crucial for long-distance signal exchange in environments with strong degradation of free signal molecules.

Noise-induced symmetry breaking has barely been unveiled on the ecological grounds, though its occurrence may elucidate mechanisms responsible for maintaining biodiversity and ecosystem stability. Here, for a network of excitable consumer-resource systems, we show that the interplay of network structure and noise intensity manifests a transition from homogeneous steady states to inhomogeneous steady states, resulting in noise-induced symmetry breaking. On further increasing the noise intensity, there exist asynchronous oscillations, leading to heterogeneity crucial for maintaining a system's adaptive capacity. The observed collective dynamics can be understood analytically in the framework of linear stability analysis of the corresponding deterministic system.

We consider the two-species Vicsek model (TSVM) consisting of two kinds of self-propelled particles, A and B, that tend to align with particles from the same species and to antialign with the other. The model shows a flocking transition that is reminiscent of the original Vicsek model: it has a liquid-gas phase transition and displays micro-phase-separation in the coexistence region where multiple dense liquid bands propagate in a gaseous background. The interesting features of the TSVM are the existence of two kinds of bands, one composed of mainly A particles and one mainly of B particles, the appearance of two dynamical states in the coexistence region: the PF (parallel flocking) state in which all bands of the two species propagate in the same direction, and the APF (antiparallel flocking) state in which the bands of species A and species B move in opposite directions. When PF and APF states exist in the low-density part of the coexistence region they perform stochastic transitions from one to the other. The system size dependence of the transition frequency and dwell times show a pronounced crossover that is determined by the ratio of the band width and the longitudinal system size. Our work paves the way for studying multispecies flocking models with heterogeneous alignment interactions.

The gravitational settling of oil droplets solubilizing in an aqueous micellar solution contained in a capillary channel is investigated. The motion of these active droplets reflects a competition between gravitational and Marangoni forces, the latter due to interfacial tension gradients generated by differences in filled-micelle concentrations along the oil-water interface. This competition is studied by varying the surfactant concentration, the density difference between the droplet and the continuous phase, and the viscosity of the continuous phase. The Marangoni force enhances the settling speed of an active droplet when compared to the Hadamard-Rybczynski prediction for a (surfactant free) droplet settling in Stokes flow. The Marangoni force can also induce lateral droplet motion, suggesting that the Marangoni and gravitational forces are not always aligned. The decorrelation rate ($\alpha$) of the droplet motion, measured as the initial slope of the velocity autocorrelation and indicative of the extent to which the Marangoni and gravitational forces are aligned during settling, is examined as a function of the droplet size: correlated motion (small values of $\alpha$) is observed at both small and large droplet radii, whereas significant decorrelation can occur between these limits. This behavior of active droplets settling in a capillary channel is in marked contrast to that observed in a dish, where the decorrelation rate increases with the droplet radius before saturating at large values of droplet radius. A simple relation for the crossover radius at which the maximal value of $\alpha$ occurs for an active settling droplet is proposed.

Within the entire mesomorphic range, high-precision dielectric anisotropy data with the high-temperature resolution is presented for a highly polar smectic-$A$ liquid crystal 8CB (octylcyanobiphenyl) as well as 8CB nanocomposites doped with both pristine multi-walled carbon nanotubes (p-MWCNTs) and carboxyl group (-COOH) functionalized MWCNTs (f-MWCNTs). The temperature variation of the nematic order parameter across both the nematic-isotropic (N-I) and the nematic–smectic-$A$ (N-Sm-$A$) phase transitions of the neat 8CB and $8\mathrm{CB}+\mathrm{MWCNT}$ nanocomposites has then been derived from the dielectric anisotropy data within the framework of the Maier-Meier theory. With the inclusion of MWCNTs, both the N-I and the N-Sm-$A$ transition temperatures have been noted to shift to lower temperatures as compared to the 8CB host. Also, for all $8\mathrm{CB}+\mathrm{MWCNT}$ nanocomposites, regardless of the surface functionalization, it has been well documented that the N-I transition is weakly first order, whereas the N-Sm-$A$ transition remains continuous within the experimental resolution. For all investigated samples, the temperature dependence of the nematic order parameter has been shown to be quasitricritical, within the experimental resolution. From the attentive inspection of the dielectric anisotropy data in the vicinity of the N-Sm-$A$ transition, the upper limits for a possible latent heat $\mathrm{\Delta }{H}_{NA}$ for the 8CB host and all $8\mathrm{CB}+\mathrm{MWCNT}$ composites, for the first time, have been derived. The so-derived $\mathrm{\Delta }{H}_{NA}$ values for all investigated samples have also been compared with those extracted from the optical birefringence data, and an excellent consistency has then been noted. The N-Sm-$A$ pretransitional anomaly has been investigated and the effective specific heat capacity exponent $\alpha$ values have been yielded from the power-law analysis of our high-resolution $\mathrm{\Delta }\varepsilon \left(T\right)$ data across the N-Sm-$A$ transition for all investigated samples. It has been well documented that the incorporation of MWCNTs to the 8CB host leaves the N-Sm-$A$ transition essentially bulklike. We discussed that, to some extent, the compliance of MWCNTs does not drive the N-Sm-$A$ transition to 3D-$XY$-like behavior, that is the strength of de Gennes coupling will remain the same for all nanocomposites. This issue can be ascribed to the weaker nature of MWCNT disorder. In this work, for the first time, high-resolution $\mathrm{\Delta }\varepsilon \left(T\right)$ data has been shown to be very adequate and offer an easy way to investigate the N-Sm-$A$ transition as compared to calorimetric methods.

Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over stochastic paths. However, estimating time-integrated quantities from real data with limited time resolution is challenging. Here, we propose a framework for accurately estimating time-integrated quantities using Bézier interpolation. We applied our approach to two dynamical inference problems: Determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes. We found that Bézier interpolation reduces the estimation bias for both dynamical inference problems. This improvement was especially noticeable for data sets with limited time resolution. Our method could be broadly applied to improve accuracy for other dynamical inference problems using finitely sampled data.

The response of a weakly absorbing isotropic medium to a sudden localized perturbation (a “splash”) is explained within the framework of linear response theory. In this theory splashes result from the interference of the collective excitations of the medium, with the outcome determined by the interplay between their phase and group velocities as well as the sign of the latter. The salient features of splashes are controlled by the existence of extremal values of the phase and the group velocities: the group velocity gives the expansion rate of the locus of the points where new wave fronts nucleate or existing ones disappear, while the phase velocity determines the large-time expansion rate of a group of wave fronts. If the group velocity is negative in a spectral range and takes on a minimal value within it, then converging wave fronts will be present in the splash. These results are relevant to the studies of several experimentally viable setups, such as a splash on the surface of deep water due to a small pebble or a raindrop, a splash in the two-dimensional electron gas caused by a short voltage pulse applied with the tip of a scanning tunneling microscope, or a bulk splash in superfluid ${}^4\mathrm{He}$ due to formation of an electron bubble. Specifically, the gross features of a splash in superfluid ${}^4\mathrm{He}$ are determined by five extremal velocities. Additionally, due to the existence of a negative group-velocity spectral range, some of the wave fronts in the superfluid splash are converging.

We investigate a universal curve in asymptotic correlation functions of off-critical systems that possess $C_{6v}$ symmetry following the argument for $C_{4v}$ symmetry in our previous paper [Phys. Rev. E 102, 032141 (2020)]. Unlike the $C_{4v}$ case, a minimal asymptotic form exists, which contains only two free parameters: the normalization constant and the modulus of the universal curve. We perform large-scale Monte Carlo simulations of the triangular lattice $Q$-state Potts model above the transition temperature. For $Q=1$, 2, 3, and 4, we successfully obtain numerical evidence that the minimal form gives the leading asymptotic behavior. We also discuss the possibility that the corrections to the minimal form are expressed using this form as a building block. From the minimal form with optimized parameters, we derive the equilibrium crystal shape of the honeycomb lattice Potts model, which is given by an algebraic curve of genus 1 and is universal among models with $C_{6v}$. Although the curve differs from those obtained in the $C_{4v}$ case, the latter curves also have genus 1. We indicate that the birational equivalence concept can play an important role in comparing asymptotic forms for different point group symmetries, for example, $C_{6v}$ and $C_{4v}$.

This work reports the different information theoretic measures, i.e., Shannon information entropy, order, disorder, complexity, and their dynamical measure for the interacting bosons in an optical lattice with both commensurate and incommensurate filling factor. We solve the many-body Schrödinger equation from first principles by multiconfigurational time-dependent Hartree method which calculates all the measures with high level of accuracy. We find for both relaxed state as well as quenched state the López-Ruiz–Mancini–Calbet (LMC) measure of complexity is the most efficient depictor of superfluid (SF) to Mott-insulator transition. In the quench dynamics, the distinct structure of LMC complexity can be used as a “figure of merit” to obtain the timescale of SF to Mott state entry, Mott holding time, and the Mott state to SF state entry in the successive cycles. We also find that fluctuations in the dynamics of LMC complexity measure for incommensurate filling clearly establish that superfluid to Mott-insulator transition is incomplete. We overall conclude that distinct structure in the complexity makes it more sensitive than the standard use of Shannon information entropy.

The coupled phase oscillator model serves as a paradigm that has been successfully used to shed light on the collective dynamics occurring in large ensembles of interacting units. It was widely known that the system experiences a continuous (second-order) phase transition to synchronization by gradually increasing the homogeneous coupling among the oscillators. As the interest in exploring synchronized dynamics continues to grow, the heterogeneous patterns between phase oscillators have received ample attention during the past years. Here, we consider a variant of the Kuramoto model with quenched disorder in their natural frequencies and coupling. Correlating these two types of heterogeneity via a generic weighted function, we systematically investigate the impacts of the heterogeneous strategies, the correlation function, and the natural frequency distribution on the emergent dynamics. Importantly, we develop an analytical treatment for capturing the essential dynamical properties of the equilibrium states. In particular, we uncover that the critical threshold corresponding to the onset of synchronization is unaffected by the location of the inhomogeneity, which, however, does depend crucially on the value of the correlation function at its center. Furthermore, we reveal that the relaxation dynamics of the incoherent state featuring the responses to external perturbations is significantly shaped by all the considered effects, thereby leading to various decaying mechanisms of the order parameters in the subcritical region. Moreover, we untangle that synchronization is facilitated by the out-coupling strategy in the supercritical region. Our study is a step forward in highlighting the potential importance of the inhomogeneous patterns involved in the complex systems, and could thus provide theoretical insights for profoundly understanding the generic statistical mechanical properties of the steady states toward synchronization.

Can strange sets arise out of quantum dynamics? We explore this question using the quantum analog of a classical impact oscillator, which consists of a forced spring-mass-damper system, with a wall it may collide against. The classical impact oscillator is known to undergo a sudden transition to chaos when the mass grazes the wall. We numerically compute the evolution of the wave function in the equivalent quantum system and investigate the dynamical signatures. The entropy of the probability density and the $L_1$ norm are used to generate real-valued time series, which are then subjected to diagnostic tests. Even though closed quantum systems with unitary evolution are incapable of showing chaotic behavior, we observe the characteristic features of strange nonchaotic dynamics in the forced system.

Cells in developing embryos reliably differentiate to attain location-specific fates, despite fluctuations in morphogen concentrations that provide positional information and in molecular processes that interpret it. We show that local contact-mediated cell-cell interactions utilize inherent asymmetry in the response of patterning genes to the global morphogen signal yielding a bimodal response. This results in robust developmental outcomes with a consistent identity for the dominant gene at each cell, substantially reducing the uncertainty in the location of boundaries between distinct fates.

We develop a mesoscopic approach to model the nonequilibrium behavior of membranes at the cellular scale. Relying on lattice Boltzmann methods, we develop a solution procedure to recover the Nernst-Planck equations and Gauss's law. A general closure rule is developed to describe mass transport across the membrane, which is able to account for protein-mediated diffusion based on a coarse-grained representation. We demonstrate that our model is able to recover the Goldman equation from first principles and show that hyperpolarization occurs when membrane charging dynamics are controlled by multiple relaxation timescales. The approach provides a promising way to characterize non-equilibrium behaviors that arise due to the role of membranes in mediating transport based on realistic three-dimensional cell geometries.

The steady streaming generated near solid walls by the periodic forcing of a viscous fluid is known to be strongly enhanced near sharp structures, owing to centrifugal effects that lead to the generation of an intense jet from the sharp tip. This flow has been shown to provide efficient active mixing in microchannels, due to strong transverse velocity. The forcing is often prescribed by acoustic transducers, but it can also be generated from low-frequency time-periodic flow ensured by mechanical vibrations. In this paper, we study the flow structure generated by low-frequency forcing (typically 10 Hz) around a sharp tip. Using direct numerical simulations, we extract both the time-periodic and steady responses within a large span of amplitude of vibrations. When the amplitude is smaller than the tip radius of curvature, we recover the flow structure observed at higher frequencies ($>1$ kHz) in previous studies, namely, an intense symmetric central jet and a quadratic dependence for the characteristic streaming velocity with the oscillating velocity $v_s\sim v_a^2$. At higher amplitudes, such a scaling no longer holds and the streaming flow pattern loses its left-right symmetry. We then analyze the mechanisms of the instability from the careful examination of the instationary flow fields, and we propose possible mechanisms for such a flow transition involving the coupling between the streaming jet and instationary vorticity.