Entropy and chemical change. I - Characterization of product /and reactant/ energy distributions in reactive molecular collisions: Information and entropy deficiency.
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Bernstein, R. B.↗
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Extensive entropy: the case of zero entropy defect
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G Livadiotis↗
A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD
The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].
High Order Physical Preserving Methods↗
Entropy Signatures of Topological Phase Transitions
We review the behavior of the entropy per particle in various two-dimensional electronic systems. The entropy per particle is an important characteristic of any many-body system that tells how the entropy of the ensemble of electrons changes if one adds one more electron. Recently, it has been demonstrated how the entropy per particle of a two-dimensional electron gas can be extracted from the recharging current dynamics in a planar capacitor geometry. These experiments pave the way to the systematic studies of entropy in various crystal systems including novel two-dimensional crystals such as gapped graphene, germanene, and silicene. Theoretically, the entropy per particle is linked to the temperature derivative of the chemical potential of the electron gas by the Maxwell relation. Using this relation, we calculate the entropy per particle in the vicinity of topological transitions in various two-dimensional electronic systems. We show that the entropy experiences quantized steps at the points of Lifshitz transitions in a two-dimensional electron gas with a parabolic energy spectrum. In contrast, in doubled-gapped Dirac materials, the entropy per particle demonstrates characteristic spikes once the chemical potential passes through the band edges. The transition from a topological to trivial insulator phase in germanene is manifested by the disappearance of a strong zero-energy resonance in the entropy per particle dependence on the chemical potential. We conclude that studies of the entropy per particle shed light on multiple otherwise hidden peculiarities of the electronic band structure of novel two-dimensional crystals.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quantum Extremal Surfaces and the Holographic Entropy Cone
Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Global and Regional Entropy Production by Radiation Estimated from Satellite Observations
Vertical profiles of shortwave and longwave irradiances computed with satellite-derived cloud properties and temperature and humidity profiles from reanalysis are used to estimate entropy production. Entropy production by shortwave radiation is computed by the absorbed irradiance within layers in the atmosphere and by the surface divided by their temperatures. Similarly, entropy production by longwave radiation is computed by emitted irradiance to space from layers in the atmosphere and surface divided by their temperatures. Global annual mean entropy production by shortwave absorption and longwave emission to space are, respectively, 0.852 and 0.928 W/sq.mK. With a steady-state assumption, entropy production by irreversible processes within the Earth system is estimated to be 0.076 W/sq.mK and by nonradiative irreversible processes to be 0.049 W/sq.mK. Both global annual mean entropy productions by shortwave absorption and longwave emission to space increase with increasing shortwave absorption (i.e., with decreasing the planetary albedo). The increase of entropy production by shortwave absorption is, however, larger than the increase of entropy production by longwave emission to space. The result implies that global annual mean entropy production by irreversible processes decreases with increasing shortwave absorption. Input and output temperatures derived by dividing the absorbed shortwave irradiance and emitted longwave irradiance to space by respective entropy production are, respectively, 282 and 259 K, which give the Carnot efficiency of the Earth system of 8.5%.
Seiji Kato↗
High-Entropy 2D Carbide MXenes: TiVNbMoC 3 and TiVCrMoC 3
Two-dimensional (2D) transition metal carbides and nitrides, known as MXenes, are a fast-growing family of 2D materials. MXenes 2D flakes have n + 1 (n = 1-4) atomic layers of transition metals interleaved by carbon/nitrogen layers, but to-date remain limited in composition to one or two transition metals. In this study, by implementing four transition metals, we report the synthesis of multi-principal-element high-entropy M 4 C 3 T x MXenes. Specifically, we introduce two high-entropy MXenes, TiVNbMoC 3 T x and TiVCrMoC 3 T x , as well as their precursor TiVNbMoAlC 3 and TiVCrMoAlC 3 high-entropy MAX phases. We used a combination of real and reciprocal space characterization (X-ray diffraction, X-ray photoelectron spectroscopy, energy dispersive X-ray spectroscopy, and scanning transmission electron microscopy) to establish the structure, phase purity, and equimolar distribution of the four transition metals in high-entropy MAX and MXene phases. We use first-principles calculations to compute the formation energies and explore synthesizability of these high-entropy MAX phases. We also show that when three transition metals are used instead of four, under similar synthesis conditions to those of the four-transition-metal MAX phase, two different MAX phases can be formed (i.e., no pure single-phase forms). This finding indicates the importance of configurational entropy in stabilizing the desired single-phase high-entropy MAX over multiphases of MAX, which is essential for the synthesis of phase-pure high-entropy MXenes. The synthesis of high-entropy MXenes significantly expands the compositional variety of the MXene family to further tune their properties, including electronic, magnetic, electrochemical, catalytic, high temperature stability, and mechanical behavior.
2D materials↗
The holographic dual of Rényi relative entropy
The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT’s. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime. Moreover, if the CFT has a semi-classical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime. In this paper, we introduce a one-parameter generalization of the relative entropy which we call refined Rényi relative entropy. We study this quantity in CFT’s and find a one-parameter generalization of the aforementioned known results about the relative entropy. We also discuss a new family of positive energy theorems in asymptotically locally AdS spacetimes that arises from the holographic dual of the refined Rényi relative entropy.
97 MATHEMATICS AND COMPUTING↗
Holographic entropy relations repackaged
We explore the structure of holographic entropy relations (associated with ‘information quantities’ given by a linear combination of entanglement entropies of spatial sub-partitions of a CFT state with geometric bulk dual). Such entropy relations can be recast in multiple ways, some of which have significant advantages. Motivated by the already-noted simplification of entropy relations when recast in terms of multipartite information, we explore additional simplifications when recast in a new basis, which we dub the K-basis, constructed from perfect tensor structures. For the fundamental information quantities such a recasting is surprisingly compact, in part due to the interesting fact that entropy vectors associated to perfect tensors are in fact extreme rays in the holographic entropy cone (as well as the full quantum entropy cone). More importantly, we prove that all holographic entropy inequalities have positive coefficients when expressed in the K-basis, underlying the key advantage over the entropy basis or the multipartite information basis.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗
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↗
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↗
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↗
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↗
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,↗
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↗
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↗
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↗