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At least 1,099 records · Page 61

Scale-invariant entropy-based theory for dynamic ordering

Dynamically Ordered self-organized dissipative structure exists in various forms and at different scales. This investigation first introduces the concept of an isolated embedding system, which embeds an open system, e.g., dissipative structure and its mass and/or energy exchange with its surroundings. Thereafter, scale-invariant theoretical analysis is presented using thermodynamic principles for Order creation, existence, and destruction. The sustainability criterion for Order existence based on its structured mass and/or energy interactions with the surroundings is mathematically defined. This criterion forms the basis for the interrelationship of physical parameters during sustained existence of dynamic Order. It is shown that the sufficient condition for dynamic Order existence is approached if its sustainability criterion is met, i.e., its destruction path is blocked. This scale-invariant approach has the potential to unify the physical understanding of universal dynamic ordering based on entropy considerations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Entropy and enthalpy of interaction between amino acid side chains in nanopores

Understanding the stabilities of proteins in nanopores requires a quantitative description of confinement induced interactions between amino acid side chains. We use molecular dynamics simulations to study the nature of interactions between the side chain pairs ALA-PHE, SER-ASN, and LYS-GLU in bulk water and in water-filled nanopores. The temperature dependence of the bulk solvent potentials of mean force and the interaction free energies in cylindrical and spherical nanopores is used to identify the corresponding entropic and enthalpic components. The entropically stabilized hydrophobic interaction between ALA and PHE in bulk water is enthalpically dominated upon confinement depending on the relative orientations between the side chains. In the case of SER-ASN, hydrogen bonded configurations that are similar in bulk water are thermodynamically distinct in a cylindrical pore, thus making rotamer distributions different from those in the bulk. Remarkably, salt bridge formation between LYS-GLU is stabilized by entropy in contrast to the bulk. Implications of our findings for confinement-induced alterations in protein stability are briefly outlined.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transition Helmholtz free energy, entropy, and heat capacity of free-standing smectic films in water: A mean-field treatment

Using the extended McMillan's mean field approach with anisotropic forces a study of both the structural and thermodynamic properties of free-standing smectic film (FSSF) in water on heating to the isotropic temperature is carried out numerically. By solving the self-consistent nonlinear equations for the order parameters, we obtained that the smectic-A-isotropic (AI) transition occurs through the series of layer-thinning transitions causing the films to thin in the stepwise manner as the temperature is increased above the bulk smectic-A-isotropic temperature T{sub AI}(bulk). With enhanced pair interactions in the bounding layers, the smectic-isotropic transition corresponds to smectic melting of the central layers. The effects of surface “enhanced” pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy and entropy, as well as the temperature dependence of the heat capacity of FSSFs, have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained – by means of optical microscopy and ellipsometry techniques – data of the temperature when the thin decylcyanobiphenyl smectic film immersing in water ruptures has been obtained.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Maximum entropy models of ecosystem functioning

Using organism-level traits to deduce community-level relationships is a fundamental problem in theoretical ecology. This problem parallels the physical one of using particle properties to deduce macroscopic thermodynamic laws, which was successfully achieved with the development of statistical physics. Drawing on this parallel, theoretical ecologists from Lotka onwards have attempted to construct statistical mechanistic theories of ecosystem functioning. Jaynes’ broader interpretation of statistical mechanics, which hinges on the entropy maximisation algorithm (MaxEnt), is of central importance here because the classical foundations of statistical physics do not have clear ecological analogues (e.g. phase space, dynamical invariants). However, models based on the information theoretic interpretation of MaxEnt are difficult to interpret ecologically. Here I give a broad discussion of statistical mechanical models of ecosystem functioning and the application of MaxEnt in these models. Emphasising the sample frequency interpretation of MaxEnt, I show that MaxEnt can be used to construct models of ecosystem functioning which are statistical mechanical in the traditional sense using a savanna plant ecology model as an example.

54 ENVIRONMENTAL SCIENCES↗

Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics

Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the 'quantum potential' that leads to the Schrödinger equation follows naturally from information geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Causation entropy from symbolic representations of dynamical systems

Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale systems are often symbolized, either because of the finite resolution of the measurement apparatus, or because of the need of statistical estimation. By algorithmic application of causation entropy, we investigated the effects of symbolization on important concepts such as Markov order and causal structure of the tent map. We uncovered that these quantities depend nonmonotonically and, most of all, sensitively on the choice of symbolization. Indeed, we show that Markov order and causal structure do not necessarily converge to their original analog counterparts as the resolution of the partitioning becomes finer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Essential roles of protein-solvent many-body correlation in solvent-entropy effect on protein folding and denaturation: Comparison between hard-sphere solvent and water

In earlier works, we showed that the entropic effect originating from the translational displacement of water molecules plays the pivotal role in protein folding and denaturation. The two different solvent models, hard-sphere solvent and model water, were employed in theoretical methods wherein the entropic effect was treated as an essential factor. However, there were similarities and differences in the results obtained from the two solvent models. In the present work, to unveil the physical origins of the similarities and differences, we simultaneously consider structural transition, cold denaturation, and pressure denaturation for the same protein by employing the two solvent models and considering three different thermodynamic states for each solvent model. The solvent-entropy change upon protein folding/unfolding is decomposed into the protein-solvent pair (PA) and many-body (MB) correlation components using the integral equation theories. Each component is further decomposed into the excluded-volume (EV) and solvent-accessible surface (SAS) terms by applying the morphometric approach. The four physically insightful constituents, (PA, EV), (PA, SAS), (MB, EV), and (MB, SAS), are thus obtained. Moreover, (MB, SAS) is discussed by dividing it into two factors. This all-inclusive investigation leads to the following results: (1) the protein-water many-body correlation always plays critical roles in a variety of folding/unfolding processes; (2) the hard-sphere solvent model fails when it does not correctly reproduce the protein-water many-body correlation; (3) the hard-sphere solvent model becomes problematic when the dependence of the many-body correlation on the solvent number density and temperature is essential: it is not quite suited to studies on cold and pressure denaturating of a protein; (4) when the temperature and solvent number density are limited to the ambient values, the hard-sphere solvent model is usually successful; and (5) even at the ambient values, however, the many-body correlation plays significant roles in the β-sheet formation and argument of relative stabilities of very similar structures of a protein. These results are argued in detail with respect to the four physically insightful constituents and the two factors mentioned above. The relevance to the absence or presence of hydrogen-bonding properties in the solvent is also discussed in detail.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spin-driven ordering of Cr in the equiatomic high entropy alloy NiFeCrCo

Spin-driven ordering of Cr in an equiatomic fcc NiFeCrCo high entropy alloy (HEA) was predicted by first-principles calculations. Ordering of Cr is driven by the reduction in energy realized by surrounding anti-ferromagnetic Cr with ferromagnetic Ni, Fe, and Co in an alloyed L1{sub 2} structure. The fully Cr-ordered alloyed L1{sub 2} phase was predicted to have a magnetic moment that is 36% of that for the magnetically frustrated random solid solution. Three samples were synthesized by milling or casting/annealing. The cast/annealed sample was found to have a low temperature magnetic moment that is 44% of the moment in the milled sample, which is consistent with theoretical predictions for ordering. Scanning transmission electron microscopy measurements were performed and the presence of ordered nano-domains in cast/annealed samples throughout the equiatomic NiFeCrCo HEA was identified.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Large entropy change accompanying two successive magnetic phase transitions in TbMn{sub 2}Si{sub 2} for magnetic refrigeration

Structural and magnetic properties in TbMn{sub 2}Si{sub 2} are studied by variable temperature X-ray diffraction, magnetization, electrical resistivity, and heat capacity measurements. TbMn{sub 2}Si{sub 2} undergoes two successive magnetic transitions at around T{sub c1} = 50 K and T{sub c2} = 64 K. T{sub c1} remains almost constant with increasing magnetic field, but T{sub c2} shifts significantly to higher temperature. Thus, there are two partially overlapping peaks in the temperature dependence of magnetic entropy change, i.e., −ΔS{sub M} (T). The different responses of T{sub c1} and T{sub c2} to external magnetic field, and the overlapping of −ΔS{sub M} (T) around T{sub c1} and T{sub c2} induce a large refrigerant capacity (RC) within a large temperature range. The large reversible magnetocaloric effect (−ΔS{sub M}{sup peak} ∼ 16 J/kg K for a field change of 0–5 T) and RC (=396 J/kg) indicate that TbMn{sub 2}Si{sub 2} could be a promising candidate for low temperature magnetic refrigeration.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Investigations of quaternary interdiffusion in a constituent system of high entropy alloys

Interdiffusion was investigated at 1000°C in a quaternary Fe-Ni-Co-Cr system, which is an essential constituent of many high-entropy alloys. The relative values of main and cross interdiffusion coefficients determined from concentrations and interdiffusion fluxes developed in a single diffusion couple indicate that significant diffusional interactions exist in this system. Thermodynamic interactions between the binary constituents were analyzed based on the activity coefficient relations and it is shown that the observed diffusional interactions of a component with others are consistent with relative thermodynamic interactions between them.

36 MATERIALS SCIENCE↗

Sign reversal of transformation entropy change in Co{sub 2}Cr(Ga,Si) shape memory alloys

In situ X-ray diffraction (XRD) measurements and compression tests were performed on Co{sub 2}Cr(Ga,Si) shape memory alloys. The reentrant martensitic transformation behavior was directly observed during the in situ XRD measurements. The high-temperature parent phase and low-temperature reentrant parent phase were found to have a continuous temperature dependence of lattice parameter, therefore suggesting that they are the same phase in nature. Moreover, compression tests were performed on a parent-phase single crystal sample; an evolution from normal to inverse temperature dependence of critical stress for martensitic transformation was directly observed. Based on the Clausius-Clapeyron analysis, a sign reversal of entropy change can be expected on the same alloy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High-entropy alloys as high-temperature thermoelectric materials

Thermoelectric (TE) generators that efficiently recycle a large portion of waste heat will be an important complementary energy technology in the future. While many efficient TE materials exist in the lower temperature region, few are efficient at high temperatures. Here, we present the high temperature properties of high-entropy alloys (HEAs), as a potential new class of high temperature TE materials. We show that their TE properties can be controlled significantly by changing the valence electron concentration (VEC) of the system with appropriate substitutional elements. Both the electrical and thermal transport properties in this system were found to decrease with a lower VEC number. Overall, the large microstructural complexity and lower average VEC in these types of alloys can potentially be used to lower both the total and the lattice thermal conductivity. These findings highlight the possibility to exploit HEAs as a new class of future high temperature TE materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Non-linear dielectric signatures of entropy changes in liquids subject to time dependent electric fields

A model of non-linear dielectric polarization is studied in which the field induced entropy change is the source of polarization dependent retardation time constants. Numerical solutions for the susceptibilities of the system are obtained for parameters that represent the dynamic and thermodynamic behavior of glycerol. The calculations for high amplitude sinusoidal fields show a significant enhancement of the steady state loss for frequencies below that of the low field loss peak. Also at relatively low frequencies, the third harmonic susceptibility spectrum shows a “hump,” i.e., a maximum, with an amplitude that increases with decreasing temperature. Both of these non-linear effects are consistent with experimental evidence. While such features have been used to conclude on a temperature dependent number of dynamically correlated particles, N{sub corr}, the present result demonstrates that the third harmonic susceptibility display a peak with an amplitude that tracks the variation of the activation energy in a model that does not involve dynamical correlations or spatial scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Entanglement entropy of electronic excitations

A new perspective into correlation effects in electronically excited states is provided through quantum information theory. The entanglement between the electron and hole quasiparticles is examined, and it is shown that the related entanglement entropy can be computed from the eigenvalue spectrum of the well-known natural transition orbital (NTO) decomposition. Non-vanishing entanglement is obtained whenever more than one NTO pair is involved, i.e., in the case of a multiconfigurational or collective excitation. An important implication is that in the case of entanglement it is not possible to gain a complete description of the state character from the orbitals alone, but more specific analysis methods are required to decode the mutual information between the electron and hole. Moreover, the newly introduced number of entangled states is an important property by itself giving information about excitonic structure. The utility of the formalism is illustrated in the cases of the excited states of two interacting ethylene molecules, the conjugated polymer para-phenylene vinylene, and the naphthalene molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High thermal stability and sluggish crystallization kinetics of high-entropy bulk metallic glasses

Metallic glasses are metastable and their thermal stability is critical for practical applications, particularly at elevated temperatures. The conventional bulk metallic glasses (BMGs), though exhibiting high glass-forming ability (GFA), crystallize quickly when being heated to a temperature higher than their glass transition temperature. This problem may potentially be alleviated due to the recent developments of high-entropy (or multi-principle-element) bulk metallic glasses (HE-BMGs). In this work, we demonstrate that typical HE-BMGs, i.e., ZrTiHfCuNiBe and ZrTiCuNiBe, have higher kinetic stability, as compared with the benchmark glass Vitreoy1 (Zr{sub 41.2}Ti{sub 13.8}Cu{sub 12.5}Ni{sub 10}Be{sub 22.5}) with a similar chemical composition. The measured activation energy for glass transition and crystallization of the HE-BMGs is nearly twice that of Vitreloy 1. Moreover, the sluggish crystallization region ΔT{sub pl-pf}, defined as the temperature span between the last exothermic crystallization peak temperature T{sub pl} and the first crystallization exothermic peak temperature T{sub pf}, of all the HE-BMGs is much wider than that of Vitreloy 1. In addition, high-resolution transmission electron microscopy characterization of the crystallized products at different temperatures and the continuous heating transformation diagram which is proposed to estimate the lifetime at any temperature below the melting point further confirm high thermal stability of the HE-BMGs. Surprisingly, all the HE-BMGs show a small fragility value, which contradicts with their low GFA, suggesting that the underlying diffusion mechanism in the liquid and the solid of HE-BMGs is different.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Coarse-grained models using local-density potentials optimized with the relative entropy: Application to implicit solvation

Bottom-up multiscale techniques are frequently used to develop coarse-grained (CG) models for simulations at extended length and time scales but are often limited by a compromise between computational efficiency and accuracy. The conventional approach to CG nonbonded interactions uses pair potentials which, while computationally efficient, can neglect the inherently multibody contributions of the local environment of a site to its energy, due to degrees of freedom that were coarse-grained out. This effect often causes the CG potential to depend strongly on the overall system density, composition, or other properties, which limits its transferability to states other than the one at which it was parameterized. Here, we propose to incorporate multibody effects into CG potentials through additional nonbonded terms, beyond pair interactions, that depend in a mean-field manner on local densities of different atomic species. This approach is analogous to embedded atom and bond-order models that seek to capture multibody electronic effects in metallic systems. We show that the relative entropy coarse-graining framework offers a systematic route to parameterizing such local density potentials. We then characterize this approach in the development of implicit solvation strategies for interactions between model hydrophobes in an aqueous environment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The large deviation principle and steady-state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗