Variations in activation energy and nuclei size during nucleation explain chiral symmetry breaking.

We show that variations in enantiomer nuclei size and activation energy during the nucleation stage of crystallization are responsible for the chiral symmetry breaking resulting in excess of one of the possible enantiomers with respect to the other. By understanding the crystallisation process as a non-equilibrium self-assembly process, we quantify the enantiomeric excess through the probability distribution of the nuclei size and activation energy variations which are obtained from the free energy involved in the nucleation stage of crystallisation. We validate our theory by comparing it to Kondepudi et al. previous experimental work on sodium chlorate crystallisation. The results demonstrate that the self-assembly of enantiomeric crystals provides an explanation for chiral symmetry breaking. These findings could have practical applications for improving the production of enantiopure drugs in the pharmaceutical industry, as well as for enhancing our understanding of the origins of life since enantiomeric amino acids and monosaccharides are the building blocks of life.

Predicting cancer stages from tissue energy dissipation.

Understanding cancer staging in order to predict its progression is vital to determine its severity and to plan the most appropriate therapies. This task has attracted interest from different fields of science and engineering. We propose a computational model that predicts the evolution of cancer in terms of the intimate structure of the tissue, considering that this is a self-organised structure that undergoes transformations governed by non-equilibrium thermodynamics laws. Based on experimental data on the dependence of tissue configurations on their elasticity and porosity, we relate the cancerous tissue stages with the energy dissipated, showing quantitatively that tissues in more advanced stages dissipate more energy. The knowledge of this energy allows us to know the probability of observing the tissue in its different stages and the probability of transition from one stage to another. We validate our results with experimental data and statistics from the World Health Organisation. Our quantitative approach provides insights into the evolution of cancer through its different stages, important as a starting point for new and integrative research to defeat cancer.

Optimal transport of active particles induced by substrate concentration oscillations.

We show the existence of a stochastic resonant regime in the transport of active colloidal particles under confinement. The periodic addition of substrate to the system causes the spectral amplification to exhibit a maximum for an optimal noise level value. The consequence of this is that particles can travel longer distances with lower fuel consumption. The stochastic resonance phenomenon found allows the identification of optimal scenarios for the transport of active particles, enabling them to reach regions that are otherwise difficult to access, and may therefore find applications in transport in cell membranes and tissues for medical treatments and soil remediation.

Chiral symmetry breaking induced by energy dissipation.

Spontaneous chiral symmetry breaking is observed in a wide variety of systems on very different scales, from the subatomic to the cosmological. Despite its generality and importance for a large number of applications, its origin is still a matter of debate. It has been shown that the existence of a difference between the energies of the intermediate states of optical enantiomers leads to disparate production rates and thus to symmetry breaking. However, it is still unclear why this occurs. We measured for the first time the optical rotation angle of NaClO3 enantiomeric crystals in solution during their formation and found that the amount of energy needed to induce the enantiomeric excess is exactly the same as the energy dissipated per mole of solid salt calculated from the entropy production obtained from the proposed model. The irreversible nature of the process leading to entropy production thus explains the chiral symmetry breaking in the salt crystals studied. The proposed method could be used to explain the formation of self-organised structures generated by self-assembly of enantiomers arising from chiral symmetry breaking, such as those emerging in the production of advanced materials and synthetic biological tissues.

Nonequilibrium thermodynamics of Janus particle self-assembly.

We compute the energetic cost of formation of Janus particle structures. Using an approach that couples particle dynamics to the evolution of fuel concentration in the medium, which we consider to be initially inhomogeneous, we show the different types of emerging structures. The energy dissipated in the formation of such structures is obtained from the entropy production rate, which is a non-monotonic function of the fraction of assembled particles and, thus, different in each self-assembly regime. An analysis of the free energy of these particles allows us to establish a thermodynamic criterion of structure formation based on the behavior of chemical potential as a function of the fraction of assembled particles.

Enhancing particle transport in deformable micro-channels.

It is shown that the action of an oscillating force on particles moving through a deformable-walled channel causes them to travel greater distances than in the case of a rigid channel. This increase in the transport efficiency is due to an intensification of the stochastic resonance effect observed in corrugated rigid channels, for which the response to the force is maximal for an optimal value of the thermal noise. The distances traveled by the particles are even larger when the oscillation of the micro-channel is synchronized with that of an applied transverse force and also when a constant external force is considered. The phenomenon found could be observed in the transport of particles through elastic porous media, in drug delivery to cancerous tissues, and in the passage of substrates through transporters in biological membranes. Our results indicate that an appropriate channel design and a suitable choice of applied forces lead to optimal scenarios for particle transport.

Gibbs thermodynamics and surface properties at the nanoscale.

Gibbs's classical thermodynamic framework approximates systems as infinitely large phases separated by infinitely thin surfaces. The range of validity of this classical framework naturally comes under scrutiny as we become interested in the properties of ever smaller systems. This Communication clarifies that while Gibbs's original framework of bulk phase thermodynamics did require modifications to describe the properties of very small (i.e., non-additive) phases, his classical framework remains fundamentally valid to describe the thermodynamic properties of surfaces. We explain why classical surface laws are applicable at the nanoscale, as suggested by simulations and confirmed by experiments. We also show that a generalized Gibbs-Tolman-Koenig-Buff equation and the resulting Tolman's law for surface tension are obtained from a classical thermodynamic analysis in the Tolman region, a region of interaction between the system and the environment.

Role of Interfacial Entropy in the Particle-Size Dependence of Thermophoretic Mobility.

We show that changes in the surface tension of a particle due to the presence of nonionic surfactants and impurities, which alter the interfacial entropy, have an impact on the value of the thermophoretic mobility. We have found the existence of different behaviors of this quantity in terms of particle size which can be summarized through a power law. For particles that are small enough, the thermophoretic mobility is a constant, whereas for larger particles it is linear in the particle radius. These results show the important role of the interfacial entropic effects on the behavior of the thermophoretic mobility.

Entropic transport in a crowded medium.

To know how liquid matter moves through a crowded medium due to the action of a force constitutes currently a problem of great practical importance, present in cases as diverse as the transport of particles through a cell membrane and through a particulate porous medium. To calculate the mass flow through the system, we present an approach that emulates the texture of the medium by using entropic barriers that the particles must overcome in order to move. The model reproduces the scaling behavior of the velocity with the force found in many systems in order to show how the scaling exponent depends on the micro-structure of the medium. Our model offers a new perspective that is able to characterize the flow of matter through the medium and may be useful in studies of nano-fluids, oil recovery, soil drainage, tissue engineering, and drug delivery.

Self-assembling outside equilibrium: emergence of structures mediated by dissipation.

A set of disordered interacting building blocks may form ordered structures by means of a self-assembling process. An external intervention in the system by adding a chemical species or by applying forces leads to different self-assembly scenarios with the appearance of new structures. For instance, the formation of microtubules, gels, virus capsides, cells and living beings among others takes place by self-assembly under nonequilibrium conditions. A general evolution criterion able to account for why nature selects some structures outside equilibrium and not others is lacking. Nevertheless, progress in the understanding of nonequilibrium self-assembly (NESA) mechanisms has been made thanks to the formulation of models that take particular situations into consideration. We review recent efforts devoted to describing self-assembly out of equilibrium and we provide a reference linking several current concepts in order to help in the development of new models and experimental studies. We hope that the knowledge of the intimate mechanisms leading to the formation of structures will make the implementation of re-configurable and bio-inspired materials possible and give a simpler perspective on the understanding of the emergence of life.

Optimizing the performance of the entropic splitter for particle separation.

Recently, it has been shown that entropy can be used to sort Brownian particles according to their size. In particular, a combination of a static and a time-dependent force applied on differently sized particles which are confined in an asymmetric periodic structure can be used to separate them efficiently, by forcing them to move in opposite directions. In this paper, we investigate the optimization of the performance of the "entropic splitter." Specifically, the splitting mechanism and how it depends on the geometry of the channel, and the frequency and strength of the periodic forcing is analyzed. Using numerical simulations, we demonstrate that a very efficient and fast separation with a practically 100% purity can be achieved by a proper optimization of the control variables. The results of this work could be useful for a more efficient separation of dispersed phases such as DNA fragments or colloids dependent on their size.

Mesoscopic non-equilibrium thermodynamic analysis of molecular motors.

We show that the kinetics of a molecular motor fueled by ATP and operating between a deactivated and an activated state can be derived from the principles of non-equilibrium thermodynamics applied to the mesoscopic domain. The activation by ATP, the possible slip of the motor, as well as the forward stepping carrying a load are viewed as slow diffusion along a reaction coordinate. Local equilibrium is assumed in the reaction coordinate spaces, making it possible to derive the non-equilibrium thermodynamic description. Using this scheme, we find expressions for the velocity of the motor, in terms of the driving force along the spacial coordinate, and for the chemical reaction that brings about activation, in terms of the chemical potentials of the reactants and products which maintain the cycle. The second law efficiency is defined, and the velocity corresponding to maximum power is obtained for myosin movement on actin. Experimental results fitting with the description are reviewed, giving a maximum efficiency of 0.45 at a myosin headgroup velocity of 5 × 10(-7) m s(-1). The formalism allows the introduction and test of meso-level models, which may be needed to explain experiments.

Entropic splitter for particle separation.

We present a particle separation mechanism which induces the motion of particles of different sizes in opposite directions. The mechanism is based on the combined action of a driving force and an entropic rectification of the Brownian fluctuations caused by the asymmetric form of the channel along which particles proceed. The entropic splitting effect shown could be controlled upon variation of the geometrical parameters of the channel and could be implemented in narrow channels and microfluidic devices.

Controlling protein crystal growth rate by means of temperature.

We have proposed a model to analyze the growth kinetics of lysozyme crystals/aggregates under non-isothermal conditions. The model was formulated through an analysis of the entropy production of the growth process which was obtained by taking into account the explicit dependence of the free energy on the temperature. We found that the growth process is coupled with temperature variations, resulting in a novel Soret-type effect. We identified the surface entropy of the crystal/aggregate as a decisive ingredient controlling the behavior of the average growth rate as a function of temperature. The behavior of the Gibbs free energy as a function of temperature is also analyzed. The agreement between theory and experiments is very good in the range of temperatures considered.

Temperature at small scales: a lower limit for a thermodynamic description.

We analyze the concept of equilibrium temperature in a set of interacting argon atoms, confined in a nanostructure, a zeolite with an intricate distribution of channels through which the atoms may move. The temperature is computed following two procedures: by averaging over the kinetic energy of the particles and over the forces acting on them. It is shown that for external surfaces and for regions which do not fall under the whole pattern of potential energy distribution, smaller than a quarter of a crystal unit cell, both temperatures, kinetic and configurational, show significant differences. The configurational temperature accounts for the different interactions on the particles in the different parts of the channels which makes them move in an energetically heterogeneous environment. The kinetic temperature is practically not affected by these inhomogeneities. The observed disparity between both temperatures disappears when averages are taken over larger regions of the zeolite. The size of these regions imposes a lower limit for a consistent thermodynamic description of a small-scale systems such as nanostructured materials, catalytic cells, and nano heat-exchangers.

Transition to irreversibility in sheared suspensions: an analysis based on a mesoscopic entropy production.

We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated with the motion of the particles. We show that the Onsager coupling between different contributions to the entropy production is responsible for the scaling of the mean square displacement on particle diameter and applied strain. We also show that the shear-induced effective diffusion coefficient depends on the volume fraction, and use lattice-Boltzmann simulations to characterize the effect through the power spectrum of particle positions for different Reynolds numbers and volume fractions. Our study gives a thermodynamic explanation of the transition to irreversibility through a pertinent analysis of the second law of thermodynamics.

Entropic stochastic resonance.

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.

Entropic particle transport in periodic channels.

The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two-dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two-dimensional dynamics can be approximated by an effective one-dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one-dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two-dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant.

Biased diffusion in confined media: test of the Fick-Jacobs approximation and validity criteria.

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

Unifying thermodynamic and kinetic descriptions of single-molecule processes: RNA unfolding under tension.

We use mesoscopic nonequilibrium thermodynamics theory to describe RNA unfolding under tension. The theory introduces reaction coordinates, characterizing a continuum of states for each bond in the molecule. The unfolding considered is so slow that one can assume local equilibrium in the space of the reaction coordinates. In the quasi-stationary limit of high sequential barriers, our theory yields the master equation of a recently proposed sequential-step model. Nonlinear switching kinetics is found between open and closed states. Our theory unifies the thermodynamic and kinetic descriptions and offers a systematic procedure to characterize the dynamics of the unfolding process.