Entropic Force Research Articles

Entropic force of cone-tethered polymers interacting with a planar surface.

Computer simulations are used to characterize the entropic force of one or more polymers tethered to the tip of a hard conical object that interact with a nearby hard flat surface. Pruned-enriched Rosenbluth method Monte Carlo simulations are used to calculate the variation of the conformational free energy F of a hard-sphere polymer with respect to the cone-tip-to-surface distance h from which the variation of the entropic force f≡|dF/dh| with h is determined. We consider the following cases: a single freely jointed tethered chain, a single semiflexible tethered chain, and several freely jointed chains of equal length each tethered to the cone tip. The simulation results are used to test the validity of a prediction by Maghrebi etal. [Maghrebi et al., Europhys. Lett. 96, 66002 (2011)0295-507510.1209/0295-5075/96/66002; Phys. Rev. E 86, 061801 (2012)1539-375510.1103/PhysRevE.86.061801] that f∝(γ_{∞}-γ_{0})h^{-1}, where γ_{0} and γ_{∞} are universal scaling exponents for the partition function of the tethered polymer for h=0 and h=∞, respectively. The measured functions f(h) are generally consistent with the predictions, with small quantitative discrepancies arising from the approximations employed in the theory. In the case of multiple tethered polymers, the entropic force per polymer is roughly constant, which is qualitatively inconsistent with the predictions.

The strange case of shear-thinning in non-Brownian suspensions

<h2>Abstract</h2> Shear thinning is generally reported in Brownian suspensions where it is understood to arise from a decrease in the relative contribution of entropic forces. However it has also been often reported in experiments with non-colloidal systems and nominally-Newtonian matrices at high volume fractions. In spite of the generality of the observations, its origin is still a matter of debate and the behaviour is difficult to reproduce in numerical simulations where shear thickening is typically observed instead. Several explanations have been proposed in recent years ranging from hidden non-Newtonian effects in the small interparticle gaps (Vázquez-Quesada et al., Phys. Rev. Lett. 117 (10), 108001 (2016), J. Non- Newt. Fluid Mech. 248, 1-7(2017)), excluded volume effects (Chatté et al. Soft Matter,14, 879-89 (2018)) and variable friction coefficients (Chatté et al.Soft Matter,14, 879-89 (2018); Tanner et al.Rheol. Acta 57:635–643 (2018); Lobry et al. J. Fluid Mech., 860, 682–710 (2019)). Another possibility that has emerged recently is related to slip occurring in the interparticle gaps at the liquid-solid interface (Kroupa et al. Phys. Chem. Chem. Phys., 19, 5979-5984 (2017); Vázquez-Quesada et al., Phys. Rev. Fluids 3 (12), 123302 (2018); Kumar et al.J. Non-Newt. Fluid Mech., 281, 104312 (2020)). In this talk I will review some of these issues and recent theories developed in this context.

Dynamics of magnetic skyrmions driven by a temperature gradient in a chiral magnet FeGe

We experimentally demonstrate the reversible motion of skyrmions driven by the controlled thermal fluctuations in a chiral magnet FeGe. A temperature gradient applied to the chiral magnet not only induces a flow of electrons but also excites a flow of magnons. Consequently, it is found that the skyrmion shows directional thermal diffusion toward two opposite directions along the gradient of temperature. We show that the skyrmions driven by the temperature gradient move from the cold terminal to the hot terminal due to the effect of magnon current induced by the temperature gradient. An obvious transverse shift of skyrmions is observed, which indicates the thermal-induced skyrmion Hall effect. Moreover, the thermal diffusion of skyrmions from the hot terminal to the cold terminal with a Hall motion as a result of competition of the magnon current, entropic force, and the spin-transfer torques induced by the thermally excited electron flow is also observed when the temperature at the hot terminal is high enough. Our results demonstrate an efficient manipulation of skyrmion dynamics by a controllable temperature gradient, which may provide a promising way for the realization of caloritronic applications based on topological spin textures.

Driven polymer translocation into a channel: Isoflux tension propagation theory and Langevin dynamics simulations

Isoflux tension propagation (IFTP) theory and Langevin dynamics (LD) simulations are employed to study the dynamics of channel-driven polymer translocation in which a polymer translocates into a narrow channel and the monomers in the channel experience a driving force ${f}_{\mathrm{c}}$. In the high driving force limit, regardless of the channel width, IFTP theory predicts $\ensuremath{\tau}\ensuremath{\propto}{f}_{\text{c}}^{\ensuremath{\beta}}$ for the translocation time, where $\ensuremath{\beta}=\ensuremath{-}1$ is the force scaling exponent. Moreover, LD data show that for a very narrow channel fitting only a single file of monomers, the entropic force due to the subchain inside the channel does not play a significant role in the translocation dynamics and the force exponent $\ensuremath{\beta}=\ensuremath{-}1$ regardless of the force magnitude. As the channel width increases the number of possible spatial configurations of the subchain inside the channel becomes significant and the resulting entropic force causes the force exponent to drop below unity.

All Nature Seemed To Be, in Perfect Harmony

it interprets market behavior in terms of entropic forces which, when expressed in quantum terms, can account for a variety of behavioral effects of the sort studied in quantum cognition and quantum decision theory

Quantum oscillations in the stock market

This paper develops a quantum harmonic oscillator model of price fluctuations in a stock market, which builds on a previously-published quantum model of supply and demand, and can be viewed as a quantized version of a classical econometrics model first proposed in 1933. An advantage of the approach is that it interprets market behavior in terms of entropic forces which, when expressed in quantum terms, can account for a variety of behavioral effects of the sort studied in quantum cognition and quantum decision theory. The model helps to interpret quantities such as force, mass, frequency and energy in a financial setting, and is consistent with observed phenomena such as the square-root behavior of price impact.

Gestalt Theory for ‘Disorder’: From Arnheim’s Ordered Chaos to Brambilla’s Entropic Art

The article revisits the concept of entropy in art as discussed by Gestalt psychologist and art theorist Rudolf Arnheim. His discussion of artworks and their reception as complex dynamic fields where the forces of entropy and orderliness counter and complete each other, are brought into dialogue with newer approaches, from the perspective of complexity theory and neuroscience, to the dynamics of perception and to entropic processes in the brain. I will argue that even though Arnheim’s observations can still be valuable for contemporary art criticism they need to be updated as they tend to overstate the tendency for order as well as the visual aspects of reception in the expense of multimodal and embodied aspects. In light of these observations, I will discuss contemporary cases of ‘entropic’ art through the moving image works of Marco Brambilla, their aesthetics as well as the ‘structural themes’ arising and the Gestalt processes involved in their reception.

4D printing of PET-G via FDM including tailormade excess third shape

In this paper, for the first time, the 4D printing capability and shape memory effect of PETG as a novel shape memory thermoplastic has been investigated with an option of emerging tailormade excess curved third shape during the shape recovery step. A self-bending through the primary printed layers was observed due to entropic force relief caused by functionally-graded polymer chain extension in each layer. Implementation of printing temperature and speed of 200◦C and 70 mm/s, respectively, results in an opaque appearance and a more curved third shape. On the other hand, a transparent appearance with a gentle curved permanent shape was achieved by the parameters of 240◦C and 10 mm/s. The observations are attributed to the effect of printing parameters on the degree of polymer chains’ extension and its difference for each layer. Both samples show an exemplary shape memory effect behavior with higher than 96 % total shape recovery.

A Cryptographic Test of Randomness, Entropy, and Brute Force Attack on the Modified Playfair Algorithm with the Novel Dynamic Matrix

One critical concern in designing a cryptographic algorithm is its randomness. The randomness test examines the quality of random numbers generated by cryptographic algorithms. In this paper, the National Institute of Standards and Technology (NIST) Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications was instrumental in assessing the security of the modified Playfair algorithm with the novel Multidimensional Element-in-Grid Sequencer (MEGS). Moreover, this study determines the level of security of the MEGS-based Playfair algorithm against brute force attacks. Simulation results revealed that the modified cryptographic algorithm could execute the encryption process with randomly generated ciphertext despite having repetitive letters in the plaintext, as evident in the frequency (monobit) test, frequency within a block test, and runs test with p-values &gt; 0.01. Further, the MEGS-based Playfair algorithm was highly resistant against attacks based on the results of the entropy test and the brute force attack analysis. Since the character keyspace of the modified algorithm is 256, attempts to break the ciphertext would cost a large amount of financial and computational resources. The use of a 16x16 dynamic matrix with matrix rotation, matrix shifting, matrix rolling, and crossover operations enhanced the performance of the Playfair algorithm, improving its resilience to attacks. Keywords—Brute force attack, MEGS-based Playfair algorithm, modified Playfair algorithm, NIST statistical test, randomness test

Formation mechanisms of fracture plugging zone and optimization of plugging particles

As formation mechanisms of plugging zone and criteria for fracture plugging remain unclear, plugging experiments and methods testing granular material mechanical properties are used to study the formation process of the plugging zone in fractured formations, analyze composition and ratios of different sizes of particles in the plugging zone, and reveal the essence and driving energy of the formation and damage of the plugging zone. New criteria for selecting lost circulation materials are proposed. The research results show that the formation of the plugging zone has undergone a process from inertial flow, elastic flow, to quasi-static flow. The plugging zone is composed of fracture mouth plugging particles, bridging particles and filling particles, and the proportion of the three types of particles is an important basis for designing drilling fluid loss control formula. The essence of the construction of the plugging zone is non-equilibrium Jamming phase transition. The response of the plugging zone particle system to pressure is driven by entropy force; the greater the entropy, the more stable the plugging zone. Lost circulation control formula optimized according to the new criteria has better plugging effect than the formula made according to conventional plugging rules and effectively improves the pressure-bearing capacity of the plugging zone. The research results provide a theoretical and technical basis for the lost circulation control of fractured formations.

Symmetry-Breaking and Self-Sorting in Block Copolymer-Based Multicomponent Nanocomposites.

Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer matrix represents an intricate interplay of enthalpic or entropic forces. Particle size largely affects the phase behavior of the nanocomposite. Theoretical studies indicate that new morphologies would emerge when the particles become comparable to the soft matrix's size, but this has rarely been supported experimentally. By designing a multicomponent blend composed of NPs, block copolymer-based supramolecules, and small molecules, a 3-D ordered lattice beyond the native BCP's morphology was recently reported when the particle is larger than the microdomain of BCP. The blend can accommodate various formulation variables. In this paper, when the particle size equals the microdomain size, a symmetry-broken phase appears in a narrow range of particle sizes and compositions, which we named the "train track" structure. In this phase, the NPs aligned into a 3-D hexagonal lattice and packed asymmetrically along the c axis, making the projection of the ac and the bc plane resemble train tracks. Computational studies show that the broken symmetry reduces the polymer chain deformation and stabilizes the metastable hexagonally perforated lamellar morphology. Given the mobility of the multicomponent blend, the system shows a self-sorting behavior: segregating into two macroscopic phases with different nanostructures based on only a few nanometers NP size differences. Smaller NPs form "train track" morphology, while larger NPs form a "simple hexagon" structure, where the NPs take a symmetric hexagonal arrangement. Detailed structural evolution and simulation studies confirm the systematic-wide cooperativity across different components, indicating the strong self-regulation of the multicomponent system.

Simulations of DNA denaturation dynamics under constrained conditions

We study the dynamics of double-stranded DNA (dsDNA) denaturation using Brownian dynamics simulations. We use a coarse-grained single nucleotide model for dsDNA which considers the helix structure. We compare the melting dynamics for free DNA of length 300 base pairs with that of a DNA of the same length but fixed from one end—mimicking DNA tethered to a substrate. We find that free DNA melts at faster rate because the entropic gain associated with denaturation is larger. Additionally, we insert the DNA in nanochannels of different widths to study the influence of the confinement on the melting dynamics. Our results suggest that there is no significant difference in the critical temperature or rate of melting when the channel width , where R g is the radius of gyration of DNA. Instead, at channel width of R g/4 we only see partial denaturation at the free DNA melting temperature. Surprisingly, this trend is reversed at higher temperature, and we find that at 110 °C tight confinement results in faster melting. This is due to the fact that confinement promotes segregation of the single-stranded segment, thereby acting as an effective entropic force aiding denaturation.

Entropic force and real-time dynamics of holographic quarkonium in a magnetic field

We continue the study of a recently constructed holographic QCD model supplemented with magnetic field. We consider the holographic dual of a quark, anti-quark pair and investigate its entropy beyond the deconfinement phase transition in terms of interquark distance, temperature and magnetic field. We obtain a clear magnetic field dependence in the strongly decreasing entropy near deconfinement and in the entropy variation for growing interquark separation. We uncover various supporting evidences for inverse magnetic catalysis. The emergent entropic force is found to become stronger with magnetic field, promoting the quarkonium dissociation. We also probe the dynamical dissociation of the quarkonium state, finding a faster dissociation with magnetic field. At least the static predictions should become amenable to a qualitative comparison with future lattice data.

Reentrant transitions in a mixture of small and big particles interacting via soft repulsive potential.

We report an observation of a temperature-controlled reentrant transition in simulations of mixtures of small and big particles interacting via a soft repulsive potential in two dimensions. As temperature increases, the system passes from a fluid mixture, to a crystal of big particles in a fluid of small particles, and back to a fluid mixture. Solidification is driven by entropy gain of small particles which overcomes the free-energy cost of confining big ones. Melting results from enhanced interpenetration of particles at high temperature which reduces the entropic forces that stabilize the crystal.

Momentum-space gravity from the quantum geometry and entropy of Bloch electrons

Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the Berry curvature, an intuitive understanding of the quantum metric is lacking. Here, we show that the quantum metric of Bloch electrons leads to a momentum-space gravity. In particular, by extending the semiclassical formulation of electron dynamics to second order, we find that the resulting velocity is modified by a geodesic term and becomes the momentum-space dual of the Lorentz force in curved space. We calculate this geodesic response for magic-angle twisted bilayer graphene and show that moir\'e systems with flat bands are ideal candidates to observe this effect. Extending this analogy with gravity further, we find that the momentum-space dual of the Einstein field equations remains sourceless for pure states, while for mixed states it acquires a source term that depends on the von Neumann entropy for small entropies. We compare this stress-energy equation with the weak-field limit of general relativity, and we conclude that the von Neumann entropy is the momentum-space dual of the gravitational potential. Consequently, the momentum-space geodesic equation for mixed states is modified by a term resembling an entropic force. Our results highlight connections between quantum geometry, momentum-space gravity, and quantum information, prompting further exploration of this dual gravity in quantum materials.

Thermal-fluctuation gradient induced tangential entropic forces in layered two-dimensional materials

Recent studies on nanomechanical devices based on low-dimensional nanomaterials have revealed several different types of thermal fluctuation gradient induced tangential entropic forces (TEFs), including expulsion force, edge force, thermophoretic force, nanodurotaxis force, etc. While all these forces originate from thermal fluctuation gradients, they can take different forms for different problems and have been treated case-by-case in the literature. Here, we develop a unified theoretical framework for TEFs in layered low-dimensional materials. In particular, we derive explicit analytical solutions for TEFs in layered two-dimensional materials and validate them with molecular dynamics simulations for various bilayers composed of graphene, graphyne, hexagonal-boron nitride (h-BN), boron-carbon-nitride (BCN), and double walled nanotubes. We present also approximate solutions to TEFs in hetero- or substrate-supported-bilayers based on a solution-guided machine learning (SGML) technique. The developed concept for TEFs is unique to nanomechanical systems and may serve as one of the founding pillars of nanomechanics.

Experimental study of laminar-to-turbulent transition in pipe flow

This paper describes an experimental study of the unforced laminar-to-turbulent transition in pipe flow. Two pipes with different length-to-diameter ratios are investigated, and the transition phenomenon is studied using pressure measurements and visual observations. The entropy change and force balance are examined, and the peak powers are measured through fast Fourier transform analysis at various Reynolds numbers. Visual observations show that the flow structure changes at the Reynolds numbers corresponding to the peak powers. There is no clear dependency of the transition on the ratio of pipe length to diameter. The flow conditions are classified as laminar flow, transitions I, II, and III, and turbulent flow, separated by Reynolds numbers of approximately 1200, 2300, 7000, and 12 000, respectively. The transition at a Reynolds number of 1200 is caused by the force balance between the laminar and turbulent flows. The other transitions are related to the flow condition in the development region upstream of the pipe flow region. That is, the laminar-to-turbulent transition in the development region affects the transition condition in the downstream pipe flow. The laminar and turbulent development length ratios derived from the entropy changes are in reasonable agreement with the formulas for both laminar and turbulent flows. At large Reynolds numbers, the laminar flow condition will be established through the creation of a laminar-flow velocity profile at the entrance to the pipe.

Magnetic Entropic Forces Emerging in the System of Elementary Magnets Exposed to the Magnetic Field.

A temperature dependent entropic force acting between the straight direct current I and the linear system (string with length of L) of N elementary non-interacting magnets/spins is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as , where r is the distance between the edge of the string and the current I, and is the Boltzmann constant; ( is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as , which is unusual for entropic forces. The effect of “entropic pressure” is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed.

Why are SNARE complexes rod-shaped?

SNARE proteins constitute the core of a cellular machinery that fuses membranes for vital processes such as exocytotic release of neurotransmitters or hormones and intracellular trafficking. Despite years of study, the mechanism remains highly controversial. Here we developed molecularly explicit simulations that fused synaptic-sized vesicle membranes on physiological millisecond timescales for the first time, and demonstrated that membrane fusion is driven by entropic forces among the rodlike SNARE complexes (SNAREpins) and membranes.

The imaginary potential and entropic force of heavy quarkonia in strongly coupled {mathcal {N}}=4 supersymmetric Yang\u2013Mills plasma on the Coulomb branch

There are two important different mechanisms, the imaginary potential and entropic force, to investigate the dissociation of heavy quarkonia. In this paper, we calculate these two quantities for static and moving quarkonia in the rotating black 3-brane Type IIB supergravity solution dual to {mathcal {N}}=4 super Yang–Mills theory on the Coulomb branch (cSYM) at strong coupling. At Tne 0 , there are two black hole branches: the large and small black hole branches. We investigate the effects of rotating parameter and rapidity for the static and moving quakonium at the large and small black hole branches. We find both mechanisms have the same results. In the large black hole branch: as T/Lambda and beta increase the thermal width decreases and so the suppression becomes stronger. In the small black hole branch: increasing T/Lambda leads to increasing the thermal width and the quarkonium dissociates harder but beta has an opposite effect.