Fate of Boltzmann's Breathers: Stokes Hypothesis and Anomalous Thermalization.

Boltzmann showed that in spite of momentum and energy redistribution through collisions, a rarefied gas confined in a isotropic harmonic trapping potential does not reach equilibrium; it evolves instead into a breathing mode where density, velocity, and temperature oscillate. This counterintuitive prediction is upheld by cold atoms experiments. Yet, are the breathers eternal solutions of the dynamics even in an idealized and isolated system? We show by a combination of hydrodynamic arguments and molecular dynamics simulations that an original dissipative mechanism is at work, where the minute and often neglected bulk viscosity eventually thermalizes the system, which thus reaches equilibrium.

Ordered ground state configurations of the asymmetric Wigner bilayer system-Revisited with unsupervised learning.

We have reanalyzed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [Antlanger et al., Phys. Rev. Lett. 117, 118002 (2016)], comprising roughly 60 000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out "by hand," we have used for the present contribution machine learning concepts, notably based on a principal component analysis and a k-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters), we were able to reanalyze these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed, we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, thereby identifying a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states.

Shortcuts to Equilibrium with a Levitated Particle in the Underdamped Regime.

We report on speeding-up equilibrium recovery in the previously unexplored general case of the underdamped regime using an optically levitated particle. We accelerate the convergence toward equilibrium by an order of magnitude compared to the natural relaxation time. We then discuss the efficiency of the studied protocols, especially for a multidimensional system. These results pave the way for optimizing realistic nanomachines with application to sensing and developing efficient nanoheat engines.

Control of Active Brownian Particles: An Exact Solution.

Control of stochastic systems is a challenging open problem in statistical physics, with a wealth of potential applications from biology to granulates. Unlike most cases investigated so far, we aim here at controlling a genuinely out-of-equilibrium system, the two dimensional active Brownian particles model in a harmonic potential, a paradigm for the study of self-propelled bacteria. We search for protocols for the driving parameters (stiffness of the potential and activity of the particles) bringing the system from an initial passivelike steady state to a final activelike one, within a chosen time interval. The exact analytical results found for this prototypical model of self-propelled particles brings control techniques to a wider class of out-of-equilibrium systems.

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics.

Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes-which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.

Shortcuts to adiabaticity for Lévy processes in harmonic traps.

Lévy stochastic processes, with noise distributed according to a Lévy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding "shortcuts to adiabaticity": After the system is prepared in a given initial stationary state, we search for time-dependent protocols for the driving external potential, such that a given final state is reached in a given, finite time. These techniques, usually employed for stochastic processes with additive Gaussian noise, are typically based on a inverse-engineering approach allowing to find exact analytical solutions for the required protocol. We generalize the approach to the wider class of Lévy stochastic processes, both in the overdamped and (for pure translations) in the underdamped regime, by finding exact equations for the relevant characteristic functions in Fourier space.

Like-Charge Attraction at the Nanoscale: Ground-State Correlations and Water Destructuring.

Like-charge attraction, driven by ionic correlations, challenges our understanding of electrostatics both in soft and hard matter. For two charged planar surfaces confining counterions and water, we prove that, even at relatively low correlation strength, the relevant physics is the ground-state one, oblivious of fluctuations. Based on this, we derive a simple and accurate interaction pressure that fulfills known exact requirements and can be used as an effective potential. We test this equation against implicit-solvent Monte Carlo simulations and against explicit-solvent simulations of cement and several types of clays. We argue that water destructuring under nanometric confinement drastically reduces dielectric screening, enhancing ionic correlations. Our equation of state at reduced permittivity therefore explains the exotic attractive regime reported for these materials, even in the absence of multivalent counterions.

Taming the Time Evolution in Overdamped Systems: Shortcuts Elaborated from Fast-Forward and Time-Reversed Protocols.

Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution toward a well chosen common intermediate state, we analytically derive a smooth protocol to connect two arbitrary states in an arbitrarily short amount of time. Not only does the reverse-engineering approach proposed in this Letter contain the current-rather limited-catalog of explicit protocols, but it also provides a systematic strategy to build the connection between arbitrary states with a physically admissible driving. Optimization and further generalizations are also discussed.

The physics of cement cohesion.

Cement is the most produced material in the world. A major player in greenhouse gas emissions, it is the main binding agent in concrete, providing a cohesive strength that rapidly increases during setting. Understanding how such cohesion emerges is a major obstacle to advances in cement science and technology. Here, we combine computational statistical mechanics and theory to demonstrate how cement cohesion arises from the organization of interlocked ions and water, progressively confined in nanoslits between charged surfaces of calcium-silicate-hydrates. Because of the water/ions interlocking, dielectric screening is drastically reduced and ionic correlations are proven notably stronger than previously thought, dictating the evolution of nanoscale interactions during cement hydration. By developing a quantitative analytical prediction of cement cohesion based on Coulombic forces, we reconcile a fundamental understanding of cement hydration with the fully atomistic description of the solid cement paste and open new paths for scientific design of construction materials.

Relaxation dynamics of two interacting electrical double-layers in a 1D Coulomb system.

We consider an out-of-equilibrium one-dimensional model for two electrical double-layers. With a combination of exact calculations and Brownian dynamics simulations, we compute the relaxation time (τ) for an electroneutral salt-free suspension, made up of two fixed colloids, withNneutralizing mobile counterions. ForNodd, the two double-layers never decouple, irrespective of their separationL; this is the regime of like-charge attraction, whereτexhibits a diffusive scaling inL2for largeL. On the other hand, for evenN,Lno longer is the relevant length scale for setting the relaxation time; this role is played by the Bjerrum length. This leads to distinctly different dynamics: forNeven, thermal effects are detrimental to relaxation, increasingτ, while they accelerate relaxation forNodd. Finally, we also show that the mean-field theory is recovered for largeNand moreover, that it remains an operational treatment down to relatively small values ofN(N> 3).

Correction: Electroosmosis as a probe for electrostatic correlations.

Correction for 'Electroosmosis as a probe for electrostatic correlations' by Ivan Palaia et al., Soft Matter, 2020, 16, 10688-10696, DOI: 10.1039/D0SM01523G.

One-dimensional colloidal model with dielectric inhomogeneity.

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.

Strong-coupling theory of counterions with hard cores between symmetrically charged walls.

By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on pointlike counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two subpopulations, one for each plate, and integrates out one subpopulation to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard-sphere overlap are unavoidable, and thus rule out configurations.

Electroosmosis as a probe for electrostatic correlations.

We study the role of ionic correlations on the electroosmotic flow in planar double-slit channels, without salt. We propose an analytical theory, based on recent advances in the understanding of correlated systems. We compare the theory with mean-field results and validate it by means of dissipative particle dynamics simulations. Interestingly, for some surface separations, correlated systems exhibit a larger flow than predicted by mean-field. We conclude that the electroosmotic properties of a charged system can be used, in general, to infer and weight the importance of electrostatic correlations therein.

Finite-time adiabatic processes: Derivation and speed limit.

Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant at both the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression or decompression situation.

Optimizing Brownian escape rates by potential shaping.

Brownian escape is key to a wealth of physico-chemical processes, including polymer folding and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates, in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under 2 different regularizations and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.

Electric double layers with surface charge modulations: Exact Poisson-Boltzmann solutions.

Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide exact analytical solutions to this nonlinear mean-field approach for the diffuse layer of ions in the vicinity of a planar or a cylindrical macroion. While previously known solutions are for homogeneously charged objects, the cases worked out exhibit a modulated surface charge-or equivalently, surface potential-on the macroion (wall) surface. In addition to asymptotic features at large distances from the wall, attention is paid to the fate of the contact theorem, relating the contact density of ions to the local wall charge density. For salt-free systems (counterions only), we make use of results pertaining to the two-dimensional Liouville equation, supplemented by an inverse approach. When salt is present, we invoke the exact two-soliton solution to the 2D sinh-Gordon equation. This leads to inhomogeneous charge patterns, that are either localized or periodic in space. Without salt, the electrostatic signature of a charge pattern on the macroion fades exponentially with distance for a planar macroion, while it decays as an inverse power law for a cylindrical macroion. With salt, our study is limited to the planar geometry and reveals that pattern screening is exponential.

Free energy of cylindrical polyions: Analytical results.

Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for low salt concentration. We obtain the exact analytical low-salt asymptotic expression for the grand potential, derived from the known properties of the exact solutions to the cylindrical PB equation. These results are relevant for understanding nucleic acid processes. In practice, our expressions are accurate for arbitrary polyion charges, provided their radius is smaller than the Debye length defined by the electrolyte.

Lattice Boltzmann electrokinetics simulation of nanocapacitors.

We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics (LBE) simulations, a lattice-based algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is achieved by a simple rule to impose electrostatic boundary conditions in a consistent way with the location of the hydrodynamic interface for stick boundary conditions. The proposed method also provides the local charge induced on the electrode by the instantaneous distribution of ions under voltage. We validate it in the low voltage regime by comparison with analytical results in two model nanocapacitors: parallel plates and coaxial electrodes. We examine the steady-state ionic concentrations and electric potential profiles (and corresponding capacitance), the time-dependent response of the charge on the electrodes, and the steady-state electro-osmotic profiles in the presence of an additional, tangential electric field. The LBE method further provides the time-dependence of these quantities, as illustrated on the electro-osmotic response. While we do not consider this case in the present work, which focuses on the validation of the method, the latter readily applies to large voltages between the electrodes, as well as to time-dependent voltages. This work opens the way to the LBE simulation of more complex systems involving electrodes and metallic surfaces, such as sensing devices based on nanofluidic channels and nanotubes, or porous electrodes.

When Random Walkers Help Solving Intriguing Integrals.

We revisit a family of integrals that delude intuition and that recently appeared in mathematical literature in connection with computer algebra package verification. We show that the remarkable properties displayed by these integrals become transparent when formulated in the language of random walks. In turn, the random walk view naturally leads to a plethora of nontrivial generalizations that are worked out. Related complex identities are also derived, without the need of explicit calculation. The crux of our treatment lies in a causality argument where a message that travels at finite speed signals the existence of a boundary.