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.

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.

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.

Radiative heat transfer between two carbon nanotubes.

We analyze the radiative heat transfer between two parallel and infinitely long carbon nanotubes (CNTs). The radiative heat exchange is due to the difference between the Poynting vectors generated by the fluctuating currents when the CNTs are at different temperatures. The radiated and absorbed Poynting vectors are expressed in terms of the correlations of the electromagnetic fields obtained from the Green's function and the fluctuation-dissipation theorem for the current density. The analysis takes into account the scattering of the fields by the nanotubes. We show that the radiative heat transfer depends not only on the distance between nanotubes, but also on their chiralities and thus on their semiconducting or metallic nature, which would allow the design of nanostructures for optimal radiative heat exchange.

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.

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.

Monte Carlo simulations in the unconstrained ensemble.

The unconstrained ensemble describes completely open systems whose control parameters are the chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using the chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up an avenue for the simulation of completely open systems exchanging heat, work, and matter with the environment.

Antiresonant driven systems for particle manipulation.

We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.

Extrasynaptic Communication.

Streams of action potentials or long depolarizations evoke a massive exocytosis of transmitters and peptides from the surface of dendrites, axons and cell bodies of different neuron types. Such mode of exocytosis is known as extrasynaptic for occurring without utilization of synaptic structures. Most transmitters and all peptides can be released extrasynaptically. Neurons may discharge their contents with relative independence from the axon, soma and dendrites. Extrasynaptic exocytosis takes fractions of a second in varicosities or minutes in the soma or dendrites, but its effects last from seconds to hours. Unlike synaptic exocytosis, which is well localized, extrasynaptic exocytosis is diffuse and affects neuronal circuits, glia and blood vessels. Molecules that are liberated may reach extrasynaptic receptors microns away. The coupling between excitation and exocytosis follows a multistep mechanism, different from that at synapses, but similar to that for the release of hormones. The steps from excitation to exocytosis have been studied step by step for the vital transmitter serotonin in leech Retzius neurons. The events leading to serotonin exocytosis occur similarly for the release of other transmitters and peptides in central and peripheral neurons. Extrasynaptic exocytosis occurs commonly onto glial cells, which react by releasing the same or other transmitters. In the last section, we discuss how illumination of the retina evokes extrasynaptic release of dopamine and ATP. Dopamine contributes to light-adaptation; ATP activates glia, which mediates an increase in blood flow and oxygenation. A proper understanding of the workings of the nervous system requires the understanding of extrasynaptic communication.

Computational Model for Membrane Transporters. Potential Implications for Cancer.

To explain the increased transport of nutrients and metabolites and to control the movement of drug molecules through the transporters to the cancer cells, it is important to understand the exact mechanism of their structure and activity, as well as their biological and physical characteristics. We propose a computational model that reproduces the functionality of membrane transporters by quantifying the flow of substrates through the cell membrane. The model identifies the force induced by conformational changes of the transporter due to hydrolysis of ATP, in ABC transporters, or by an electrochemical gradient of ions, in secondary transporters. The transport rate is computed by averaging the velocity generated by the force along the paths followed by the substrates. The results obtained are in accordance with the experiments. The model provides an overall framework for analyzing the membrane transport proteins that regulate the flows of ions, nutrients and other molecules across the cell membranes, and their activities.

A Criterion for the Formation of Nonequilibrium Self-Assembled Structures.

Is there a criterion able to determine the type of structures formed in a nonequilibrium self-assembly process? This important question has a clear answer when the process takes place under equilibrium conditions: structures emerge at minimum values of the free energy. Experiments, however, have shown that when self-assembly takes place outside equilibrium, they do not appear at those free energy minima but rather at optimal values of structural parameters. On the basis of these observations, we propose a selection criterion for which structures come up at the minima of a nonequilibrium free energy that takes into account the energy needed to change their configuration. The criterion is able to predict the formation and configuration of structures such as Liesegang rings and patterns in magnetic colloids and could constitute a powerful tool to understand the synthesis of advanced materials, enantiomers, and nanoparticles.

A Legendre-Fenchel Transform for Molecular Stretching Energies.

Single-molecular polymers can be used to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. We have recently verified using molecular-dynamics simulations that isometric and isotensional stretching of a small polymer result in Helmholtz and Gibbs stretching energies, which are not related to a Legendre transform, as they are for sufficiently long polymers. This disparity has also been observed experimentally. Using molecular dynamics simulations of polyethylene-oxide, we document for the first time that the Helmholtz and Gibbs stretching energies can be related by a Legendre-Fenchel transform. This opens up a possibility to apply this transform to other systems which are small in Hill's sense.

Statistical Mechanics at Strong Coupling: A Bridge between Landsberg's Energy Levels and Hill's Nanothermodynamics.

We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill's nanothermodynamics.

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.