Entropic Force Research Articles

Thermodynamics of Thorium(IV) complexes with N-methylethylenediamine-N,Nʹ,Nʹ-triacetate in aqueous solutions: Potentiometry and microcalorimetry

The thermodynamic parameters of the complexes of Th with N-methylethylenediamine-N,Nʹ,Nʹ-triacetic acid (MEDTA; denoted as H3L with three dissociable protons) were studied. Potentiometry and microcalorimetry were used to determine formation constants and enthalpies, respectively. Thermodynamic analysis revealed two successively formed complexes, namely, ThL+ and ThL22− (L3− denotes the totally deprotonated MEDTA). Results indicated that both complexation reactions were exothermic and driven by entropic force. The first stepwise reaction (Th4+ ​+ ​L3− = ThL+) was mainly driven by entropy with minimal effect on enthalpy change. The second stepwise reaction (ThL+ ​+ ​L3− = ThL22−) was more exothermic and showed less entropic change than the first stepwise reaction. The strong chelation of MEDTA would inhibit the hydrolysis of Th4+ and increase solubility.

Dark Universe phenomenology from Yukawa potential?

We argue that the effect of cold dark matter in the cosmological setup can be explained by the coupling between the baryonic matter particles in terms of the long-range force having a graviton mass mg via the Yukawa gravitational potential. Such a quantum-corrected Yukawa-like gravitational potential is characterized by the coupling parameter α, the wavelength parameter λ, which is related to the graviton mass via mg=ħ/(λc), that determines the range of the force and, finally, a Planck length quantity l0 that makes the potential regular at the centre. The modified Friedmann equations are obtained using Verlinde’s entropic force interpretation of gravity based on the holographic scenario and the equipartition law of energy. The parameter α modifies the Newton’s constant as Geff=G(1+α). Interestingly, we find an equation that relates the dark matter density, dark energy density, and baryonic matter density. It is given by ΩD=2ΩBΩΛ(1+z)3. We argue that dark matter is an apparent effect as no dark matter particle exists in this picture. Furthermore, the dark energy is also related to graviton mass and α; in particular, we point out that the cosmological constant can be viewed as a self-interaction effect between gravitons. We further show a precise correspondence with Verlinde’s emergent gravity theory, and due to the long-range force, the theory can be viewed as a non-local gravity theory. To this end, we performed the phase space analyses and estimated λ≃103 [Mpc] and α≃0.04, respectively. Finally, from these values, for the graviton mass, we get mg≃10−68 kg, and cosmological constant Λ≃10−52m−2. Further, we argue how this theory reproduces the MOND phenomenology on galactic scales via the acceleration of Milgrom a0≃10−10m/s2.

Entropic force for quantum particles

Entropic force has been drawing the attention of theoretical physicists following E Verlinde’s work in 2011 to derive Newton’s second law and Einstein’s field equations of general relativity. In this paper, we extend the idea of entropic force to the distribution of quantum particles. Starting from the definition of Shannon entropy for continuous variables, here we have derived quantum osmotic pressure as well as the consequent entropic forces for bosonic and fermionic particles. The entropic force is computed explicitly for a pair of bosons and fermions. The low temperature limit of this result show that the entropic force for bosons is similar to Hooke’s law of elasticity revealing the importance of this idea in the formation of a Bose–Einstein condensate. For fermions, the low temperature limit boils down to the well known Neumann’s radial force and also reveals the Pauli’s exclusion principle. The classical limit of the entropic force between quantum particles is then discussed. As a further example, the entropic force for quantum particles in noncommutative space is also computed. The result reveals a violation of the Pauli exclusion principle for fermions in noncommutative space.

BEHAVIOR OF q-DEFORMED QUANTUM PARTICLE STATISTICS ON THE HOLOGRAPHIC SCREEN

In this study, we propose an approach to investigate the relationship between MOND theory and the holographic principle by incorporating q-deformed theory. We first present a brief overview of Verlinde's entropic gravity assumption, which suggests that gravity can be interpreted as an entropic force arising from the statistical mechanics of quantum fields. Some thermo-statistical properties of q-deformed fermion gas model in two spatial dimensions are introduced. At the low-temperature limit, we derive the q-deformed thermal energy and analyze the impacts of fermionic q-deformation on MOND theory. Specifically, we consider the q-deformed Fermi-Dirac statistics of the bits on the holographic screen and examine MOND theory depending on q-deformed acceleration scale. Deformed Friedmann equation is studied by taking into account Friedmann–Robertson–Walker (FRW) universe. This equation shows a modified identification of the evolution of the universe that is compatible with both MOND theory and the holographic principle

Toward a Bio-Organon: A model of interdependence between energy, information and knowledge in living systems

What is an organism? In the absence of a fundamental biological definition, what constitutes a living organism, whether it is a unicellular microbe, a multicellular being or a multi-organismal society, remains an open question. New models of living systems are needed to address the scale of this question, with implications for the relationship between humanity and planetary ecology. Here we develop a generic model of an organism that can be applied across multiple scales and through major evolutionary transitions to form a toolkit, or bio-organon, for theoretical studies of planetary-wide physiology. The tool identifies the following core organismic principles that cut across spatial scale: (1) evolvability through self-knowledge, (2) entanglement between energy and information, and (3) extrasomatic “technology” to scaffold increases in spatial scale. Living systems are generally defined by their ability to self-sustain against entropic forces of degradation. Life “knows” how to survive from the inside, not from its genetic code alone, but by utilizing this code through dynamically embodied and functionally specialized flows of information and energy. That is, entangled metabolic and communication networks bring encoded knowledge to life in order to sustain life. However, knowledge is itself evolved and is evolving. The functional coupling between knowledge, energy and information has ancient origins, enabling the original, cellular “biotechnology,” and cumulative evolutionary creativity in biochemical products and forms. Cellular biotechnology also enabled the nesting of specialized cells into multicellular organisms. This nested organismal hierarchy can be extended further, suggesting that an organism of organisms, or a human “superorganism,” is not only possible, but in keeping with evolutionary trends.

Coherent states for generalized uncertainty relations and their cosmological implications

We study coherent states associated with a generalized uncertainty principle (GUP). Our particular focus is on the negative deformation parameter β. We show that the ensuing coherent state can be identified with Tsallis’ probability amplitude with the non-extensivity parameter q being a monotonically increasing function of β. Furthermore, for β < 0, we reformulate the GUP in terms of a one-parameter class of Tsallis entropy based uncertainty relations, which are again saturated by the GUP coherent states. We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing to study the quasi-classical regime of GUP in terms of non-extensive thermostatistics. We bolster this claim by discussing a generalization of Verlinde’s entropic force and the ensuing implications in the late-inflation epoch. The corresponding dependence of the β parameter on the cosmological time is derived for the reheating epoch. The obtained β is consistent with both values predicted by string-theory models and the naturalness principle.

Engineered entropic forces allow ultrastrong dynamical backaction.

When confined within an optical cavity light can exert strong radiation pressure forces. Combined with dynamical backaction, this enables important processes, such as laser cooling, and applications ranging from precision sensors to quantum memories and interfaces. However, the magnitude of radiation pressure forces is constrained by the energy mismatch between photons and phonons. Here, we overcome this barrier using entropic forces arising from the absorption of light. We show that entropic forces can exceed the radiation pressure force by eight orders of magnitude and demonstrate this using a superfluid helium third-sound resonator. We develop a framework to engineer the dynamical backaction from entropic forces, applying it to achieve phonon lasing with a threshold three orders of magnitude lower than previous work. Our results present a pathway to exploit entropic forces in quantum devices and to study nonlinear fluid phenomena such as turbulence and solitons.

Structural Preferences Shape the Entropic Force of Disordered Protein Ensembles.

Intrinsically disordered protein regions (IDRs) make up over 30% of the human proteome and exist in a dynamic conformational ensemble instead of a native, well-folded structure. Tethering IDRs to a surface (for example, the surface of a well-folded region of the same protein) can reduce the number of accessible conformations in these ensembles. This reduces the ensemble's conformational entropy, generating an effective entropic force that pulls away from the point of tethering. Recent experimental work has shown that this entropic force causes measurable, physiologically relevant changes to protein function. But how the magnitude of this force depends on IDR sequence remains unexplored. Here, we use all-atom simulations to analyze how structural preferences in IDR ensembles contribute to the entropic force they exert upon tethering. We show that sequence-encoded structural preferences play an important role in determining the magnitude of this force: compact, spherical ensembles generate an entropic force that can be several times higher than more extended ensembles. We further show that changes in the surrounding solution's chemistry can modulate the IDR entropic force strength. We propose that the entropic force is a sequence-dependent, environmentally tunable property of terminal IDR sequences.

Entropic contribution of ACE2 glycans to RBD binding

The spike protein of the SARS-CoV-2 virus (the causative agent of COVID-19) recognizes the host cell by binding to the peptidase domain (PD) of the extracellular receptor angiotensin-converting enzyme 2 (ACE2). A variety of carbohydrates could be attached to the six asparagines in the PD, resulting in a heterogeneous population of ACE2 glycoforms. Experiments have shown that the binding affinity of glycosylated and deglycosylated ACE2 to the virus is virtually identical. In most cases, the reduction in glycan size correlates with stronger binding, which suggests that volume exclusion, and hence entropic forces, determine the binding affinity. Here, we quantitatively test the entropy-based hypothesis by developing a lattice model for the complex between ACE2 and the SARS-CoV-2 spike protein receptor-binding domain (RBD). Glycans are treated as branched polymers with only volume exclusion, which we justify using all-atom molecular dynamics simulations in explicit water. We show that the experimentally measured changes in the ACE2-RBD dissociation constants for a variety of engineered ACE2 glycoforms are in reasonable agreement with our theory, thus supporting our hypothesis. However, a quantitative recovery of all the experimental data could require weak attractive interactions.

The effect of scatter of polymer chain length on strength

A polymer network fractures by breaking covalent bonds, but the experimentally measured strength of the polymer network is orders of magnitude lower than the strength of covalent bonds. We investigate the effect of statistical variation of the number of links in polymer chains on strength using a parallel chain model. Each polymer chain is represented by a freely-jointed chain, with a characteristic J-shaped force–extension curve. The chain carries entropic forces for most of the extension and carries covalent forces only for a narrow range of extension. The entropic forces are orders of magnitude lower than the covalent forces. Chains with a statistical distribution of the number of links per chain are pulled between two rigid parallel plates. Chains with fewer links attain covalent forces and rupture at smaller extensions, while chains with more links still carry entropic forces. We compute the applied force on the rigid plates as a function of extension and define the strength of the parallel chain model by the maximum force divided by the total number of chains. With the J-shaped force–extension curve of each chain, even a small scatter in the number of links per chain greatly reduces the strength of the parallel chain model. We further show that the strength of the parallel chain model relates to the scatter in the number of links per chain according to a power law.

Contact Guidance Drives Upward Cellular Migration at the Mesoscopic Scale.

Cancer metastasis is associated with increased cancer incidence, recurrence, and mortality. The role of cell contact guidance behaviors in cancer metastasis has been recognized but has not been elucidated yet. The contact guidance behavior of cancer cells in response to topographical constraints is identified using microgrooved substrates with varying dimensions at the mesoscopic scale. Then, the cell morphology is determined to quantitatively analyze the effects of substrate dimensions on cells contact guidance. Cell density and migrate velocity signatures within the cellular population are determined using time-lapse phase-contrast microscopy. The effect of soluble factors concentration is determined by culturing cells upside down. Then, the effect of cell-substrate interaction on cell migration is investigated using traction force microscopy. With increasing depth and decreasing groove width, cell elongation and alignment are enhanced, while cell spreading is inhibited. Moreover, cells display preferential distribution on the ridges, which is found to be more pronounced with increasing depth and groove width. Determinations of cell density and migration velocity signatures reveal that the preferential distribution on ridges is caused by cell upward migration. Combined with traction force measurement, we find that migration toward ridges is governed by different cell-substrate interactions between grooves and ridges caused by geometrical constraints. Interestingly, the upward migration of cells at the mesoscopic scale is driven by entropic maximization. The mesoscopic cell contact guidance mechanism based on the entropic force driven theory provides basic support for the study of cell alignment and migration along healthy tissues with varying size, thereby aiding in the prediction of cancer metastasis. The online version contains supplementary material available at 10.1007/s12195-023-00766-y.

Hiking down the Free Energy Landscape Using Sequential Solvent and Thermal Processing for Versatile Ordering of Block Copolymer Films.

The kinetics and morphology of the ordering of block copolymer (BCP) films are highly dependent on the processing pathway, as the enthalpic and entropic forces driving the ordering processes can be quite different depending on process history. We may gain some understanding and control of this variability of BCP morphology with processing history through a consideration of the free energy landscape of the BCP material and a consideration of how the processing procedure moves the system through this energy landscape in a way that avoids having the system becoming trapped into well-defined metastable minima having a higher free energy than the target low free energy ordered structure. It is well known that standard thermal annealing (TA) of BCPs leads to structures corresponding to a well-defined stable free energy minimum; however, the BCP must be annealed for a very long time before the target low free energy structures can be achieved. Herein, we show that the same target low-energy structure can be achieved relatively quickly by subjecting as-cast films to an initial solvent annealing [direct immersion annealing (DIA) or solvent vapor annealing (SVA)] procedure, followed by a short period of TA. This process relies on lowering the activation energy barrier by reducing the glass-transition temperature through DIA (or SVA), followed by a multi-interface chain rearrangement through sequential TA. This energy landscape approach to ordering should be applicable to the process design for ordering many other complex materials.

Modulating Entropic Driving Forces to Promote High Lithium Mobility in Solid Organic Electrolytes

Modulating Entropic Driving Forces to Promote High Lithium Mobility in Solid Organic Electrolytes

The Road to Buenos Aires Is Paved with Good Design: Worldmaking Fantasies and the Latin American Industrial Design Exhibition

ABSTRACT In 1970, Argentinian industrialists and cultural entrepreneurs sought to harness industrial design to reenergize a stalled economy. In collaboration with the International Council and the Department of Architecture and Design of the Museum of Modern Art, they worked to bring to Buenos Aires more than 400 objects of MoMA’s design collection. Spearheaded by Emilio Ambasz, the exhibition 20th Century Industrial Design would effectively reproduce the New York institution in Buenos Aires. Amid entropic forces dissolving the social cohesion of Argentine society, MoMA sought to champion a revised version of Good Design in a cultural battle for the souls of Latin American consumers.

Holographic imaginary potential of a quark antiquark pair in the presence of gluon condensation

For a moving heavy quark antiquark (QQ) in a quark gluon plasma (QGP), we use gauge/gravity duality to study both real and imaginary parts of the potential ( operatorname{Re}{V}_{Qoverline{Q}} and operatorname{Im}{V}_{Qoverline{Q}} respectively) in a gluon condensate (GC) theory. The complex potential is derived from the Wilson loop by considering the thermal fluctuations of the worldsheet of the Nambu-Goto holographic string. We calculate operatorname{Re}{V}_{Qoverline{Q}} and operatorname{Im}{V}_{Qoverline{Q}} in both cases where the axis of the moving Qoverline{Q} pair is transverse and parallel with respect to its direction of movement in the plasma. Using the renormalization scheme for the operatorname{Re}{V}_{Qoverline{Q}} , we find that the inclusion of GC increases the dissociation length while rapidity has the opposite effect. While for the operatorname{Im}{V}_{Qoverline{Q}} , we observe that by considering the effect of GC, the operatorname{Im}{V}_{Qoverline{Q}} is generated for larger distance thus decreasing quarkonium dissociation, while rapidity has opposite effect. In particular, as the value of GC decreases in the deconfined phase, the operatorname{Im}{V}_{Qoverline{Q}} is generated for smaller distance thus enhancing quarkonium dissociation, and at high temperatures it is nearly not modified by GC, consistent with previous findings of the entropic force.

Initial Effect of Temperature Rise on α-Synuclein Aggregation – Entropic Forces Drive the Exposure of Protein Hydrophobic Groups Probed by Fluorescence Spectroscopy

The aberrant formation of α-synuclein (Syn) aggregates, varying in size, structure and morphology, has been linked to the development of Parkinson’s disease. In the early stages of Syn aggregation, large protein amyloid aggregates with sizes > 100 nm in hydrodynamic radius have been noticed. These low overall abundant large Syn aggregates are notoriously difficult to study by conventional biophysical methods. Due to the growing importance of studying the early stages of Syn aggregation, we developed a strategy to achieve this purpose, which is the study of the initial effect of the Syn protein aqueous solutions temperature rise. Therefore, the increase of the Syn aqueous solutions entropy by the initial effect of the temperature rise led to the exposure of the protein hydrophobic tyrosyl groups by not interfering with this amyloid protein aggregation. As an attempt to interpret the degree of the referred protein tyrosyl groups exposure, the classic rotameric conformations of the Nα-acetyl-L-tyrosinamide (NAYA) parent compound were used. For both NAYA and Syn, it was determined that the classic rotameric conformations involving the tyrosyl groups indeed accounted for their exposure under steady-state conditions of fluorescence, for lowest molecular species concentrations investigated at least. In this situation, Syn aggregation was observed. For the higher NAYA and Syn concentrations studied, the referred classic rotameric conformation were insufficient in such referred steady-state conditions and, for Syn, in particular, fluorescence anisotropy measurements revealed that less protein aggregation occurs along with its delay. Overall, the developed strategy by focusing on the initial effect of the temperature rise of Syn aqueous solutions in lower concentrations is suitable for informing us about the degree of this protein aggregation in solution.

Entropy and its significance in transport of ions through the cell membrane

The aim of this paper is to present the concept of entropy in a simple way and to show its key importance in the transport processes of ions through the cell membrane using the latest discoveries in biophysics. Using a real-life example, we show how processes within a system lead to an increase in entropy. We also show how this entropy increase is directly related to the irreversibility of the process, and how it defines the arrow of time (direction of the flow of time). Using an abstract example, we clarify the meaning of the concept of disorder in a system, which is often used in defining entropy by connecting it with the number of microstates that realise a macroscopic state of a system. The importance of entropy in transport processes of ions through the cell membrane is considered. We show that passive transport processes through the cell membrane are the result of an entropy increase in the cell membrane-transported substance system. A model of active ion transport through the cell membrane following Rubi et al. (2017) is presented. The force that transports ions through the channel in the transport protein arises due to the entropy gradient formed along the transport channel, which is a consequence of the funnel shape of the channel. The entropic force is proportional to the ratio of the ion-available cross-sections of the exit and entrance surface of the channel. That means that only a very funnel-shaped channel can produce a sufficiently large force on the ions to overcome the concentration gradient of the substance. We analyse the final result for the force of entropy in the limits of a very wide and very narrow channel and find that the entropic force is proportional to the ratio of the areas of the exit to entrance surfaces of the channel, i.e., when the channel is very wide, while it becomes high as the width of the channel tends to the ion diameter, i.e., when the channel is very narrow. We explicitly explain how the presented model solves several fundamental questions about the active transport of substances: how is energy, a scalar quantity, converted into the directional motion of the ion (a vector quantity), how does energy drive ions considering that the point of release of energy is far from the point of binding of an ion in a transport protein and finally, how does energy, which is released in a very limited space, transport the ions over a very large spatial scale.

Structural preferences modulate the entropic force exerted by disordered proteins.

When tethered to surfaces such as lipid vesicles or well-folded proteins, polymers exert an entropic force that pulls against the point of tethering. This is because the motions produced by the protein's thermal fluctuations push against and away from the tethered surface. Intrinsically disordered protein regions (IDRs) commonly exist at the termini of proteins. When tethered to protein or membrane surfaces, IDRs were shown to exert an entropic force that is thought to largely depend on their length. However, IDPs are not homopolymers: their sequences can be complex and their conformational ensembles have structural preferences that will affect their average shape. We hypothesize that such IDR structural preferences also affect the entropic force exerted by the sequence. To test this hypothesis, we use all-atom simulations and an enhanced sampling strategy to quantify the entropic force exerted by over 100 IDR sequences. We find that IDRs with compact ensembles tend to induce a stronger entropic force than expanded IDRs. We also find that solution condition changes will alter IDR ensemble structure and thus alter the magnitude of the entropic force. Our work indicates that the structural preferences of IDRs, coupled with their interaction with the solution condition, can act together to dramatically increase the entropic force of some, but not all, IDRs.

Simulations on physiological timescales show SNAREs drive membrane fusion by entropic forces.

SNARE proteins are the core of the cellular machinery that fuses membranes for fundamental processes such as neurotransmitter or hormone release. The mechanism of SNARE-mediated fusion is controversial. Fusion is widely thought driven by the ∼60 kT zippering energy of SNARE complexation, and a minimum number of SNAREs is thought required. However, experiment suggests complexation occurs after microseconds (Kubelka et al., 2004; Xi et al., 2012), much faster than the millisecond timescales of fusion, and the reported numerical requirements vary widely.

Dispersion and orientation patterns in nanorod-infused polymer melts.

Introducing nanorods into a polymeric matrix can enhance the physical and mechanical properties of the resulting material. In this paper, we focus on understanding the dispersion and orientation patterns of nanorods in an unentangled polymer melt, particularly as a function of nanorod concentration, using molecular dynamics simulations. The system is comprised of flexible polymer chains and multi-thread nanorods that are equilibrated in the NPT ensemble. All interactions are purely repulsive except for those between polymers and rods. Results with attractive vs repulsive polymer-rod interactions are compared and contrasted. The concentration of rods has a direct impact on the phase behavior of the system. At lower concentrations, rods phase separate into nematic clusters, whereas at higher concentrations more isotropic and less structured rod configurations are observed. A detailed examination of the conformation of the polymer chains near the rod surface shows extension of the chains along the director of the rods (especially within clusters). The dispersion and orientation of the nanorods are a result of the competition between depletion entropic forces responsible for the formation of rod clusters, the enthalpic effects that improve mixing of rods and polymer, and entropic losses of polymers interpenetrating rod clusters.