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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Effective entropy of quantum fields coupled with gravity

Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Entropy-driven order in an array of nanomagnets

Long-range ordering is typically associated with a decrease in entropy. Yet, it can also be driven by increasing entropy in certain special cases. Here we demonstrate that artificial spin-ice arrays of single-domain nanomagnets can be designed to produce such entropy-driven order. We focus on the tetris artificial spin-ice structure, a highly frustrated array geometry with a zero-point Pauling entropy, which is formed by selectively creating regular vacancies on the canonical square ice lattice. We probe thermally active tetris artificial spin ice both experimentally and through simulations, measuring the magnetic moments of the individual nanomagnets. Furthermore, we find two-dimensional magnetic ordering in one subset of these moments, which we demonstrate to be induced by disorder (that is, increased entropy) in another subset of the moments. In contrast with other entropy-driven systems, the discrete degrees of freedom in tetris artificial spin ice are binary and are both designable and directly observable at the microscale, and the entropy of the system is precisely calculable in simulations. This example, in which the system’s interactions and ground-state entropy are well defined, expands the experimental landscape for the study of entropy-driven ordering.

36 MATERIALS SCIENCE↗
DOE OSTI2018

High-Entropy Alloys (HEA): Fundamentals and Applications

This book provides a systematic and comprehensive description of high-entropy alloys (HEAs). The authors summarize key properties of HEAs from the perspective of both fundamental understanding and applications, which are supported by in-depth analyses. The book also contains computational modeling in tackling HEAs, which help elucidate the formation mechanisms and properties of HEAs from various length and time scales.<br>High-entropy alloys (HEAs) [1,2] loosely refer to multi-principal-element solid solution alloys due to their high configurational entropy, in contrast to traditional alloys, which focus on the edge or corner of phase diagrams with one principal component. The unique compositions and the resulting attractive properties of HEAs have stimulated growing research interest due to scientific curiosity and potential industrial applications [3,4]. In order to balance the properties for targeted applications, the microstructure of HEAs can be a single phase or multiphases, and traditional physical metallurgy principles have been applied to develop a variety of HEAs, including high-entropy stainless steels, high-entropy superalloys, high-entropy refractory alloys, high-entropy light-weight alloys, high-entropy oxides, high-entropy metallic compounds, etc. However, great challenges still remain in the fundamental understanding of HEAs formation and their properties, and potential high-performance HEAs are yet to be explored. This special issue is meant to collect contributions from authors working in the various fields of HEAs to timely disseminate the rapid progress in this fascinating and expanding class of advanced materials.

Gao, Michael↗
NASA NTRS2003

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

Tao, Wei-Kuo↗
DOE OSTI2018

Exploring the effects of climatic variables on monthly precipitation variation using a continuous wavelet-based multiscale entropy approach

Highlights: • Developed a wavelet transform entropy approach to study precipitation. • Multiscale entropy values were the basis for precipitation regionalization. • Various entropy-based bands were introduced to segregate the CWME values for each cluster. • The relationship between changes of CWME and mean monthly precipitation were investigated. • Central rain gauges of each cluster were used for further analysis. Understanding precipitation on a regional basis is an important component of water resources planning and management. The present study outlines a methodology based on continuous wavelet transform (CWT) and multiscale entropy (CWME), combined with self-organizing map (SOM) and k-means clustering techniques, to measure and analyze the complexity of precipitation. Historical monthly precipitation data from 1960 to 2010 at 31 rain gauges across Iran were preprocessed by CWT. The multi-resolution CWT approach segregated the major features of the original precipitation series by unfolding the structure of the time series which was often ambiguous. The entropy concept was then applied to components obtained from CWT to measure dispersion, uncertainty, disorder, and diversification of subcomponents. Based on different validity indices, k-means clustering captured homogenous areas more accurately, and additional analysis was performed based on the outcome of this approach. The 31 rain gauges in this study were clustered into 6 groups, each one having a unique CWME pattern across different time scales. The results of clustering showed that hydrologic similarity (multiscale variation of precipitation) was not based on geographic contiguity. According to the pattern of entropy across the scales, each cluster was assigned an entropy signature that provided an estimation of the entropy pattern of precipitation data in each cluster. Based on the pattern of mean CWME for each cluster, a characteristic signature was assigned, which provided an estimation of the CWME of a cluster across scales of 1–2, 3–8, and 9–13 months relative to other stations. The validity of the homogeneous clusters demonstrated the usefulness of the proposed approach to regionalize precipitation. Further analysis based on wavelet coherence (WTC) was performed by selecting central rain gauges in each cluster and analyzing against temperature, wind, Multivariate ENSO index (MEI), and East Atlantic (EA) and North Atlantic Oscillation (NAO), indeces. The results revealed that all climatic features except NAO influenced precipitation in Iran during the 1960–2010 period.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Routes to fractality and entropy in Liesegang systems

Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF{sub 2} and PbI{sub 2} Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF{sub 2} and PbI{sub 2} Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids

Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW{sub 16}). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW{sub 20}), silicon (SW{sub 21}), and water (SW{sub 23.15} or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S{sub trip}, is also studied. S{sub trip} is a good entropy estimator for liquids where pair and triplet correlations are important such as Ge and Si, but loses accuracy for purely pair-dominated liquids, like LJ fluid, or near the crystallization temperature (T{sub thr}). Since local tetrahedral order is compatible with both liquid and crystalline states, the reorganisation of tetrahedral liquids is accompanied by a clear rise in the pair, triplet, and thermodynamic contributions to the heat capacity, resulting in the heat capacity anomaly. In contrast, the pair-dominated liquids show increasing dominance of triplet correlations on approaching crystallization but no sharp rise in either the pair or thermodynamic heat capacities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Data-driven Minimum Entropy Control for Stochastic Nonlinear Systems using the Cumulant-Generating Function

Here, we present a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.

42 ENGINEERING↗
DOE OSTI2025

Entropy of the Quantum–Classical Interface: A Potential Metric for Security

Hybrid quantum–classical systems are emerging as key platforms in quantum computing, sensing, and communication technologies, but the quantum–classical interface (QCI)—the boundary enabling these systems—introduces unique and largely unexplored security vulnerabilities. This position paper proposes using entropy-based metrics to monitor and enhance security, specifically at the QCI. We present a theoretical security outline that leverages well-established information-theoretic entropy measures, such as Shannon entropy, von Neumann entropy, and quantum relative entropy, to detect anomalous behaviors and potential breaches at the QCI. By linking entropy fluctuations to scenarios of practical relevance—including quantum key distribution, quantum sensing, and hybrid control systems—we promote the potential value and applicability of entropy-based security monitoring. While explicitly acknowledging practical limitations and theoretical assumptions, we argue that entropy-based metrics provide a complementary approach to existing security methods, inviting further empirical studies and theoretical refinements that can strengthen future quantum technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The evolution of gas giant entropy during formation by runaway accretion

We calculate the evolution of gas giant planets during the runaway gas accretion phase of formation, to understand how the luminosity of young giant planets depends on the accretion conditions. We construct steady-state envelope models, and run time-dependent simulations of accreting planets with the code Modules for Experiments in Stellar Astrophysics. We show that the evolution of the internal entropy depends on the contrast between the internal adiabat and the entropy of the accreted material, parametrized by the shock temperature T {sub 0} and pressure P {sub 0}. At low temperatures (T{sub 0}≲300–1000 K, depending on model parameters), the accreted material has a lower entropy than the interior. The convection zone extends to the surface and can drive a high luminosity, leading to rapid cooling and cold starts. For higher temperatures, the accreted material has a higher entropy than the interior, giving a radiative zone that stalls cooling. For T{sub 0}≳2000 K, the surface–interior entropy contrast cannot be accommodated by the radiative envelope, and the accreted matter accumulates with high entropy, forming a hot start. The final state of the planet depends on the shock temperature, accretion rate, and starting entropy at the onset of runaway accretion. Cold starts with L≲5×10{sup −6} L{sub ⊙} require low accretion rates and starting entropy, and the temperature of the accreting material needs to be maintained close to the nebula temperature. If instead the temperature is near the value required to radiate the accretion luminosity, 4πR{sup 2}σT{sub 0}{sup 4}∼(GM M-dot /R), as suggested by previous work on radiative shocks in the context of star formation, gas giant planets form in a hot start with L∼10{sup −4} L{sub ⊙}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The Holographic Entropy Cone

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Programming entropy production hotspots via interaction patterning

Dissipation in soft matter and living systems is highly heterogeneous, giving rise to complex local entropy production patterns. Recent work has identified the connection between local entropy production and locally extractable amount of work. This suggests that locally produced entropy can be recovered to power nanorobots and biological machines, prompting the need for efficient strategies to modulate and fine-tune local entropy production. In this work, we propose to program entropy production hotspots by leveraging local interaction patterns and test this approach in simulations of a fluid driven through a nanopore or past an obstacle. Here, the results show that patterning the surface of the pore with a repulsive patch gives rise to an entropy production hotspot around the patch, while an attractive patch leads to an entropy production cold spot. Varying the strength of the interaction and width of the patch enables modulating the hotness and extent of the hot spot. In flows past interaction patterned-obstacles, we show that the combined effects of steric hindrance and attraction allows to program a specific entropy production map, thereby opening the door to the precise powering of nanomachines.

Desgranges, Caroline [University of Massachusetts,↗
DOE OSTI2023

Channel capacity: limitation of entropy rate during cell signal transduction

Cellular signal transduction is mediated through chain activation reactions involving signalling molecules. Information thermodynamics may be a promising approach for quantifying signal transduction. A cell signal is transduced through the signal molecule activation as a step of a signal transduction cascade. In each step, two types of entropy can be defined. First, the signal transduction was defined using thermodynamic entropy production during the chemical activation of signal molecules. Second, the chronology was described as a code string, and the logarithm of the number of signal code strings corresponded to the information entropy. Finally, the total entropy during signal transduction was determined by summing the two entropies. When maximising the total entropy, the total entropy rate per signalling molecule concentration was found to be consistent independently of each transduction step (i.e., signal molecule types). Consequently, the speed limit of the entropy rate can be calculated, providing the capacity, which is an essential property of the signal transduction cascade. The theory introduced here is expected to provide a basic framework for understanding new methods of discovering signal cascades and intracellular signal transduction.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: i. reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements; ii. the conformational entropy of folding of β 2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state; iii. backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy); iv. the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β 2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

Science & Technology - Other Topics↗
DOE OSTI2019

Diagonal entropy and topological phase transitions in extended Kitaev chains

We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and Majorana zero modes. Both the finite size scaling law and block scaling law of the diagonal entropy are studied, which indicates that the diagonal entropy demonstrates volume effect. The parameter of volume term is regarded as the diagonal entropy density, which can identify the critical points of symmetry-protected topological phase transitions efficiently in the studied models, even for those with higher winding numbers. The formulation of block scaling law and the capability of diagonal entropy density in detecting topological phase transitions are independent of the chosen bases. In order to manifest the advantage of diagonal entropy, we also calculate the global entanglement, which cannot show clear signatures of the topological phase transitions. This work provides a new quantum-informatic approach to characterize the feature of the topologically ordered states and may motivate a deep understanding of the quantum coherence and diagonal entropy in various condensed matter systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Relating different quantum generalizations of the conditional Rényi entropy

Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here, we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Rényi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Rényi entropies and derive a new entropic uncertainty relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Entropy generation from hydrodynamic mixing in inertial confinement fusion indirect-drive targets

The increase in entropy from the physical mixing of two adjacent materials in inertial confinement fusion (ICF) implosions and gas-filled hohlraums is analytically assessed. An idealized model of entropy generation from the mixing of identical ideal-gas particles across a material interface in the presence of pressure and temperature gradients is applied. Physically, mix-driven entropy generation refers to the work done by the gases in expanding into a larger common volume from atomic mixing under the condition of no internal energy change, or work needed to restore the initial unmixed state. Furthermore, the effect of a mix-generated entropy increase is analytically shown to lead to less compression of the composite ICF fluid under adiabatic conditions. The amount of entropy generation is estimated to be ~10 J for a Rayleigh–Taylor-induced micrometer-scale annular mixing layer between the solid deuterium–tritium fuel and (undoped) high-density carbon pusher of an imploding capsule at the National Ignition Facility (NIF). This level of entropy generation is consistent with lower-than-expected fuel compressions measured on the NIF [Hurricane et al., Phys. Plasmas 26, 052704 (2019)]. The degree of entropy increase from mixing of high-Z hohlraum wall material and low-Z, moderate- to high-density gas fills is estimated to lead to ~100 kJ of heat generation for NIF-scale experiments [Moody et al., Phys. Plasmas 21, 056317 (2014)]. This value represents a significant fraction of the inferred missing x-ray drive energy based on observed delays in capsule implosion times compared with mainline simulations [Jones et al., Phys. Plasmas 19, 056315 (2012)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Studies on the structure and the magnetic properties of high-entropy spinel oxide (MgMnFeCoNi)Al 2 O 4

The study of high-entropy materials has attracted enormous interest since they could show new functional properties that are not observed in their related parent phases. Here, we report single crystal growth, structure, thermal transport, and magnetic property studies on a novel high-entropy oxide with the spinel structure (MgMnFeCoNi)Al 2 O 4 . We have successfully grown high-quality single crystals of this high-entropy oxide using the optical floating zone growth technique for the first time. The sample was confirmed to be a phase pure high-entropy oxide using x-ray diffraction and energy-dispersive spectroscopy. Through magnetization measurements, we found (MgMnFeCoNi)Al 2 O 4 exhibits a cluster spin glass state, though the parent phases show either antiferromagnetic ordering or spin glass states. Furthermore, we also found that (MgMnFeCoNi)Al 2 O 4 has much greater thermal expansion than its CoAl 2 O 4 parent compound using high resolution neutron Larmor diffraction. We further investigated the structure of this high-entropy material via Raman spectroscopy and extended x-ray absorption fine structure spectroscopy (EXAFS) measurements. From Raman spectroscopy measurements, we observed (MgMnFeCoNi)Al 2 O 4 to display a combination of the active Raman modes in its parent compounds with the modes shifted and significantly broadened. This result, together with the varying bond lengths probed by EXAFS, reveals severe local lattice distortions in this high-entropy phase. Additionally, we found a substantial decrease in thermal conductivity and suppression of the low temperature thermal conductivity peak in (MgMnFeCoNi)Al 2 O 4 , consistent with the increased lattice defects and strain. These findings advance the understanding of the dependence of thermal expansion and transport on the lattice distortions in high-entropy materials.

36 MATERIALS SCIENCE↗