Thermodynamic Insights into Symmetry Breaking: Exploring Energy Dissipation across Diverse Scales.

Symmetry breaking is a phenomenon that is observed in various contexts, from the early universe to complex organisms, and it is considered a key puzzle in understanding the emergence of life. The importance of this phenomenon is underscored by the prevalence of enantiomeric amino acids and proteins.The presence of enantiomeric amino acids and proteins highlights its critical role. However, the origin of symmetry breaking has yet to be comprehensively explained, particularly from an energetic standpoint. This article explores a novel approach by considering energy dissipation, specifically lost free energy, as a crucial factor in elucidating symmetry breaking. By conducting a comprehensive thermodynamic analysis applicable across scales, ranging from elementary particles to aggregated structures such as crystals, we present experimental evidence establishing a direct link between nonequilibrium free energy and energy dissipation during the formation of the structures. Results emphasize the pivotal role of energy dissipation, not only as an outcome but as the trigger for symmetry breaking. This insight suggests that understanding the origins of complex systems, from cells to living beings and the universe itself, requires a lens focused on nonequilibrium processes.

Enhancing carrier flux for efficient drug delivery in cancer tissues.

Ultrasound focused toward tumors in the presence of circulating microbubbles improves the delivery of drug-loaded nanoparticles and therapeutic outcomes; however, the efficacy varies among the different properties and conditions of the tumors. Therefore, there is a need to optimize the ultrasound parameters and determine the properties of the tumor tissue important for the successful delivery of nanoparticles. Here, we propose a mesoscopic model considering the presence of entropic forces to explain the ultrasound-enhanced transport of nanoparticles across the capillary wall and through the interstitium of tumors. The nanoparticles move through channels of variable shape whose irregularities can be assimilated to barriers of entropic nature that the nanoparticles must overcome to reach their targets. The model assumes that focused ultrasound and circulating microbubbles cause the capillary wall to oscillate, thereby changing the width of transcapillary and interstitial channels. Our analysis provides values for the penetration distances of nanoparticles into the interstitium that are in agreement with experimental results. We found that the penetration increased significantly with increasing acoustic intensity as well as tissue elasticity, which means softer and more deformable tissue (Young modulus lower than 50 kPa), whereas porosity of the tissue and pulse repetition frequency of the ultrasound had less impact on the penetration length. We also considered that nanoparticles can be absorbed into cells and to extracellular matrix constituents, finding that the penetration length is increased when there is a low absorbance coefficient of the nanoparticles compared with their diffusion coefficient (close to 0.2). The model can be used to predict which tumor types, in terms of elasticity, will successfully deliver nanoparticles into the interstitium. It can also be used to predict the penetration distance into the interstitium of nanoparticles with various sizes and the ultrasound intensity needed for the efficient distribution of the nanoparticles.

Strong Coupling and Nonextensive Thermodynamics.

We propose a Hamiltonian-based approach to the nonextensive thermodynamics of small systems, where small is a relative term comparing the size of the system to the size of the effective interaction region around it. We show that the effective Hamiltonian approach gives easy accessibility to the thermodynamic properties of systems strongly coupled to their surroundings. The theory does not rely on the classical concept of dividing surface to characterize the system's interaction with the environment. Instead, it defines an effective interaction region over which a system exchanges extensive quantities with its surroundings, easily producing laws recently shown to be valid at the nanoscale.

Negative Thermophoretic Force in the Strong Coupling Regime.

Negative thermophoresis (a particle moving up the temperature gradient) is a somewhat counterintuitive phenomenon which has thus far eluded a simple thermostatistical description. The purpose of this Letter is to show that a thermodynamic framework based on the formulation of a Hamiltonian of mean force has the descriptive ability to capture this interesting and elusive phenomenon in an unusually elegant and straightforward fashion. We propose a mechanism that describes the advent of a thermophoretic force acting from cold to hot on systems that are strongly coupled to a nonisothermal heat bath. When a system is strongly coupled to the heat bath, the system's eigenenergies E_{j} become effectively temperature dependent. This adjustment of the energy levels allows the system to take heat from the environment, +d⟨E_{j}⟩, and return it as work, -d⟨TdE_{j}/dT⟩. This effect can make the temperature dependence of the effective energy profile nonmonotonic. As a result, particles may experience a force in either direction depending on the temperature.

The Soret coefficient from the Faxén theorem for a particle moving in a fluid under a temperature gradient.

We compute the Soret coefficient for a particle moving through a fluid subjected to a temperature gradient. The viscosity and thermal conductivity of the particle are in general different from those of the solvent and its surface tension may depend on temperature. We find that the Soret coefficient depends linearly on the derivative of the surface tension with respect to temperature and decreases in accordance with the ratios between viscosities and thermal conductivities of particle and solvent. Additionally, the Soret coefficient also depends on a parameter which gives the ratio between Marangoni and shear stresses, a dependence which results from the local stresses inducing a heat flux along the particle surface. Our results are compared to those obtained by using the Stokes value for the mobility in the calculation of the Soret coefficient and in the estimation of the radius of the particle. We show cases in which these differences may be important. The new expression of the Soret coefficient can systematically be used for a more accurate study of thermophoresis.

Driving an electrolyte through a corrugated nanopore.

We characterize the dynamics of a z - z electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated with externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We show here that the linear transport coefficients are particularly sensitive to the geometry and the conductive properties of the channel walls when the Debye length is comparable to the channel width. In this regime, we found that one pair of off-diagonal Onsager matrix elements increases with the corrugation of the channel transport, in contrast to all other elements which are either unaffected by or decrease with increasing corrugation. Our results have a possible impact on the design of blue-energy devices as well as on the understanding of biological ion channels through membranes.

Radiative Heat Shuttling.

We demonstrate the existence of a shuttling effect for the radiative heat flux exchanged between two bodies separated by a vacuum gap when the chemical potential of photons or the temperature difference is modulated. We show that this modulation typically gives rise to a supplementary flux which superimposes to the flux produced by the mean gradient, enhancing the heat exchange. When the system displays a negative differential thermal resistance, however, the radiative shuttling contributes to insulate the two bodies from each other. These results pave the way for a novel strategy for an active management of radiative heat exchanges in nonequilibrium systems.

Nonequilibrium self-assembly induced Liesegang rings in a non-isothermal system.

We propose a model to show the formation of Liesegang rings under non-isothermal conditions. The model formulates reaction-diffusion equations for all components intervening in the process together with an evolution equation for the temperature. The reactive parts in these equations follow from the analysis of the non-equilibrium self-assembly (NESA) process undergone by the meso-particles which make up the patterns. The solution of these equations enables us to know the concentration of each component, the spherical structures diameter, and the system temperature as a function of time and radial position. The values found for the structures diameter and the rings position are in agreement with the experiments. The results for the system temperature with peaks at the rings positions suggest that heat accumulates at these positions as a consequence of the dissipation inherent to the NESA process. Our model enables us to rationalize how from non-homogeneous initial conditions a transient self-organization process involving formation of self-assembled structures may produce macroscopic patterns. It can, in general, be used to analyze pattern formation due to diffusion-reaction-precipitation processes with potential applications in the design of advanced materials.

Entropic Stabilization of Cas4 Protein SSO0001 Predicted with Popcoen.

Popcoen is a method for configurational entropy estimation of proteins based on machine-learning. Entropy is predicted with an artificial neural network which was trained on simulation trajectories of a large set of representative proteins. Popcoen is extremely fast compared to other approaches based on the sampling of a multitude of microstates. Consequently, Popcoen can be incorporated into a large class of protein software which currently neglects configurational entropy for performance reasons. Here, we apply Popcoen to various conformations of the Cas4 protein SSO0001 of Sulfolobus solfataricus, a protein that assembles to a decamer of known toroidal shape. We provide numerical evidence that the native state (NAT) of a SSO0001 monomer has a similar structure to the protomers of the oligomer, where NAT of the monomer is stabilized mainly entropically. Due to its large amount of configurational entropy, NAT has lower free energy than alternative conformations of very low enthalpy and solvation free-energy. Hence, SSO0001 serves as an example case where neglecting configurational entropy leads to incorrect conclusion. Our results imply that no refolding of the subunits is required during oligomerization which suggests that configurational entropy is employed by nature to largely enhance the rate of assembly.

Testing the mutual information expansion of entropy with multivariate Gaussian distributions.

The mutual information expansion (MIE) represents an approximation of the configurational entropy in terms of low-dimensional integrals. It is frequently employed to compute entropies from simulation data of large systems, such as macromolecules, for which brute-force evaluation of the full configurational integral is intractable. Here, we test the validity of MIE for systems consisting of more than m = 100 degrees of freedom (dofs). The dofs are distributed according to multivariate Gaussian distributions which were generated from protein structures using a variant of the anisotropic network model. For the Gaussian distributions, we have semi-analytical access to the configurational entropy as well as to all contributions of MIE. This allows us to accurately assess the validity of MIE for different situations. We find that MIE diverges for systems containing long-range correlations which means that the error of consecutive MIE approximations grows with the truncation order n for all tractable n ≪ m. This fact implies severe limitations on the applicability of MIE, which are discussed in the article. For systems with correlations that decay exponentially with distance, MIE represents an asymptotic expansion of entropy, where the first successive MIE approximations approach the exact entropy, while MIE also diverges for larger orders. In this case, MIE serves as a useful entropy expansion when truncated up to a specific truncation order which depends on the correlation length of the system.

Theory of Casimir Forces without the Proximity-Force Approximation.

We analyze both the attractive and repulsive Casimir-Lifshitz forces recently reported in experimental investigations. By using a kinetic approach, we obtain the Casimir forces from the power absorbed by the materials. We consider collective material excitations through a set of relaxation times distributed in frequency according to a log-normal function. A generalized expression for these forces for arbitrary values of temperature is obtained. We compare our results with experimental measurements and conclude that the model goes beyond the proximity-force approximation.

Entropically induced asymmetric passage times of charged tracers across corrugated channels.

We analyze the diffusion of charged and neutral tracers suspended in an electrolyte embedded in a channel of varying cross section. Making use of systematic approximations, the diffusion equation governing the motion of tracers is mapped into an effective 1D equation describing the dynamics along the longitudinal axis of the channel where its varying-section is encoded as an effective entropic potential. This simplified approach allows us to characterize tracer diffusion under generic confinement by measuring their mean first passage time (MFPT). In particular, we show that the interplay between geometrical confinement and electrostatic interactions strongly affect the MFTP of tracers across corrugated channels hence leading to alternative means to control tracers translocation across charged pores. Finally, our results show that the MFPTs of a charged tracer in opposite directions along an asymmetric channel may differ We expect our results to be relevant for biological as well synthetic devices whose dynamics is controlled by the detection of diluted tracers.

Anomalous law of cooling.

We analyze the temperature relaxation phenomena of systems in contact with a thermal reservoir that undergoes a non-Markovian diffusion process. From a generalized Langevin equation, we show that the temperature is governed by a law of cooling of the Newton's law type in which the relaxation time depends on the velocity autocorrelation and is then characterized by the memory function. The analysis of the temperature decay reveals the existence of an anomalous cooling in which the temperature may oscillate. Despite this anomalous behavior, we show that the variation of entropy remains always positive in accordance with the second law of thermodynamics.

Entropic electrokinetics: recirculation, particle separation, and negative mobility.

We show that when particles are suspended in an electrolyte confined between corrugated charged surfaces, electrokinetic flows lead to a new set of phenomena such as particle separation, mixing for low-Reynolds micro- and nanometric devices, and negative mobility. Our analysis shows that such phenomena arise, for incompressible fluids, due to the interplay between the electrostatic double layer and the corrugated geometrical confinement and that they are magnified when the width of the channel is comparable to the Debye length. Our characterization allows us to understand the physical origin of such phenomena, therefore, shedding light on their possible relevance in a wide variety of situations ranging from nano- and microfluidic devices to biological systems.

Communication: system-size scaling of Boltzmann and alternate Gibbs entropies.

It has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression S(G)(E) = k ln Σ(E' < E)Ω(E') examined by Gibbs. Here, we show that SG either is equivalent to S in the macroscopic limit or becomes independent of the energy exponentially fast as the system size increases. The resulting exponential scaling makes the realistic use of SG unfeasible and leads in general to temperatures that are inconsistent with the notions of hot and cold.

Confined Brownian ratchets.

We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.

Field emission in vacuum resonant tunneling heterostructures with high current densities.

We analyse the steady-state thermal regime of a one-dimensional triode resonant tunnelling structure. The high currents generated by resonant tunnelling produce a large amount of heat that could damage the structure. Establishing the conditions under which it can operate at optimum efficiency is therefore a problem of great relevance for applications. The tunnel current is found via eigenvalues of the Schrödinger equation in quantum wells. By calculating the current generated in the device and using the energy conservation law in the electrodes, the temperature reached is obtained for different types of electrodes and the importance of heat conduction and thermal radiation is analysed. In the cases discussed, conduction is dominant. When the electrode material is copper, the temperature reached is similar to that of the thermostat for a wide range of electrode lengths, whereas when the cathode material is diamond-graphite and the anode material is copper, the temperature increases significantly as a function of length. The results obtained allow the temperature to be controlled for optimum performance of the field-emitting triode structures.

On the thermodynamic efficiency of Ca²âº-ATPase molecular machines.

Experimental studies have shown that the activity of the reconstituted molecular pump Ca(2+)-ATPase strongly depends on the thickness of the supporting bilayer. It is thus expected that the bilayer structure will have an impact on the thermodynamic efficiency of this nanomachine. Here, we introduce a nonequilibrium-thermodynamics theoretical approach to estimate the thermodynamic efficiency of the Ca(2+)-ATPase from analysis of available experimental data about ATP hydrolysis and Ca(2+) transport. We find that the entropy production, i.e., the heat released to the surroundings under working conditions, is approximately constant for bilayers containing phospholipids with hydrocarbon chains of 18-22 carbon atoms. Our estimates for the heat released during the pump operation agree with results obtained from separate calorimetric experiments on the Ca(2+)-ATPase derived from sarcoplasmic reticulum. We show that the thermodynamic efficiency of the reconstituted Ca(2+)-ATPase reaches a maximum for bilayer thicknesses corresponding to maximum activity. Surprisingly, the estimated thermodynamic efficiency is very low, ∼12%. We discuss the significance of this result as representative of the efficiency of other nanomachines, and we address the influence of the experimental set-up on such a low efficiency. Overall, our approach provides a general route to estimate thermodynamic efficiencies and heat dissipation in experimental studies of nanomachines.

Thermomolecular orientation of nonpolar fluids.

We investigate the response of molecular fluids to temperature gradients. Using nonequilibrium molecular dynamics computer simulations we show that nonpolar diatomic fluids adopt a preferred orientation as a response to a temperature gradient. We find that the magnitude of this thermomolecular orientation effect is proportional to the strength of the temperature gradient and the degree of molecular anisotropy, as defined by the different size or mass of the molecular atomic sites. We show that the preferred orientation of the molecules follows the same trends observed in the Soret effect of binary mixtures. We argue this is a general effect that should be observed in a wide range of length scales.

Far-from-equilibrium processes without net thermal exchange via energy sorting.

Many important processes at the microscale require far-from-equilibrium conditions to occur, as in the functioning of mesoscopic bioreactors, nanoscopic rotors, and nanoscale mass conveyors. Achieving such conditions, however, is typically based on energy inputs that strongly affect the thermal properties of the environment and the controllability of the system itself. Here, we present a general class of far-from-equilibrium processes that suppress the net thermal exchange with the environment by maintaining the Maxwell-Boltzmann velocity distribution intact. This new phenomenon, referred to as ghost equilibrium, results from the statistical cancellation of superheated and subcooled nonequilibrated degrees of freedom that are autonomously generated through a microscale energy sorting process. We provide general conditions to observe this phenomenon and study its implications for manipulating energy at the microscale. The results are applied explicitly to two mechanistically different cases, an ensemble of rotational dipoles and a gas of trapped particles, which encompass a great variety of common situations involving both rotational and translational degrees of freedom.