STATISTICAL THERMODYNAMICS OF NONUNIFORM FLUIDS
Statistical thermodynamic properties of nonuniform fluids
THERMODYNAMIC PROPERTY↗
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STATISTICAL THERMODYNAMICS OF NONUNIFORM FLUIDS
Statistical evaluation of low order distribution functions and thermodynamic properties of nonuniform equilibrium flow
DISTRIBUTION FUNCTION↗
Statistical thermodynamics of A-B-A block copolymers. I
A-B-A block copolymers statistical thermodynamics, describing postulated microstructure theoretical model for phase transition prediction
Leary, D. F.↗
Circuit complexity and functionality: A statistical thermodynamics perspective
Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (“wormhole”) connecting the two sides of an anti-de Sitter “eternal” black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length—an important problem in cryptography—as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with “gases of gates.” This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.
Science & Technology - Other Topics↗
Gibbs' third variational principle in statistical thermodynamics
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Brown, W. B.↗
Equilibrium Statistical Thermodynamics of a Many-Particle System Coupled to an External Scalar Field
The equilibrium thermodynamics of a many-particle assembly in the presence of an external scalar field is examined. Two types of scalar coupling are considered: an external field coupled to the particle density and an external scalar field coupled to the energy density. It is shown that the broken translational and rotational invariance of the system due to the external field is reflected in the macroscopic physics by loss of the usual extensivity property of the system and by means of anisotropy in the response of the system to changes in the system lengths or to the system shape. In addition, the assumptions used in local equilibrium analyses are shown to be incorrect in principle. Nonlocal effects due to the external field must be included in the determination of the equation of state. Simple model calculations for a system in an external gravitational field and an externally imposed temperature field are presented as illustrations.
Salvino, R. E.↗
Thermodynamics and statistical mechanics
The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.
Source record↗
Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives
Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.
42 ENGINEERING↗
Statistics and thermodynamics of fracture
A probabilistic model of the fracture processes unifying the phenomenological study of long term strength of materials, fracture mechanics and statistical approaches to fracture is briefly outlined. The general framework of irreversible thermodynamics is employed to model the deterministic side of the failure phenomenon. The stochastic calculus is used to account for thg failure mechanisms controlled by chance; particularly, the random roughness of fracture surfaces.
Chudnovsky, A.↗
The photon gas formulation of thermal radiation
A statistical consideration of the energy, the linear momentum, and the angular momentum of the photons that make up a thermal radiation field was presented. A general nonequilibrium statistical thermodynamics approach toward a macroscopic description of thermal radiation transport was developed and then applied to the restricted equilibrium statistical thermostatics derivation of the energy, linear momentum, and intrinsic angular momentum equations for an isotropic photon gas. A brief treatment of a nonisotropic photon gas, as an example of the results produced by the nonequilibrium statistical thermodynamics approach, was given. The relativistic variation of temperature and the invariance of entropy were illustrated.
Ried, R. C., Jr.↗
Physical concepts in the development of constitutive equations
Proposed viscoplastic material models include in their formulation observed material response but do not generally incorporate principles from thermodynamics, statistical mechanics, and quantum mechanics. Numerous hypotheses were made for material response based on first principles. Many of these hypotheses were tested experimentally. The proposed viscoplastic theories and the experimental basis of these hypotheses must be checked against the hypotheses. The physics of thermodynamics, statistical mechanics and quantum mechanics, and the effects of defects, are reviewed for their application to the development of constitutive laws.
Cassenti, B. N.↗
Hadron thermodynamics in relativistic nuclear collisions
Various phenomenological models based on statistical thermodynamical considerations were used to fit the experimental data at high P sub T to a two temperature distribution. Whether this implies that the two temperatures belong to two different reaction mechanisms, or consequences of Lorentz-contraction factor, or related in a fundamental way to the intrinsic thermodynamics of Space-Time can only be revealed by further theoretical and experimental investigations of high P sub T phenomena in extremely energetic hadron-hadron collisions.
Ammiraju, P.↗
Macroscopic and bulk-controlled elastic modes in an interaction of interstitial alcali metal cations within a face-centered cubic crystalline fullerine
The calculations in a majority of previous works for the fulleride (AqC-60) crystals were performed within the framework of the rigid-lattice model, neglecting the distortion relaxation of the host fullerene (C-60) crystal caused by the interstitial alkali-metal (A) cations. However, an each cation is a source of a static distortion field, and the resulting field is a superposition of such fields generated by all cations. This is a reason why the host-crystal distortions depend on the A-cations configurations, i.e. on a type of a spatial bulk distribution of interstitial cations. The given paper seeks to find a functional relation between the amplitudes of the doping-induced structure-distortion waves and of static concentration ones. A semiphenomenological model is constructed here within the scope of statistical-thermodynamic treatment and using the lattice-statistics simulation method(*). In this model the effects due to the presence of q solute A cations over available interstices (per unit cell) on the static inherent reorientation and/or displacements of the solvent molecules from the 'average-lattice' sites' as well as on the lattice parameter a of a elastically-anysotropic 'cubic' C-60 crystal are taken into account.
Tatarenko, Valentine A.↗
Proton production in relativistic heavy ion collisions; comparison with a thermodynamical model
Experimental results concerning proton production in nuclear collisions, obtained at Saturne with the Diogene 4 pi facility, are compared with the predictions of a thermodynamical model, using collective velocity distributions combined with a statistical thermodynamics in local rest frames. Experimental differential cross sections for alpha + nucleus and Neon + nucleus central collisions at incident energies between 200 and 800 MeV per nucleon are well reproduced by the model, for an angular range 30-110 degrees in the laboratory system. Extracted values of the temperatures are compared with those given by other authors.
NASA Program Biomedical Research↗
New Dimension in Ab Initio Electronic Structure Theory: Temperature, Pressure, and Chemical Potential
Ab initio electronic structure theory has transformed gas-phase molecular science with its predictive ability. In the attempt to bring such predictive ability to macroscopic systems and condensed matter, the theory must integrate quantum mechanics with statistical thermodynamics, so that thermodynamic functions such as free energy, internal energy, entropy, and chemical potentials are computed as functions of temperature in a systematically converging series of approximations. Here, a general, versatile strategy of elevating ab initio electronic structure theory to nonzero temperatures is introduced and discussed.
74 ATOMIC AND MOLECULAR PHYSICS↗
Ensemble Effects on Hydroxide Bond Dissociation Free Energies in Polyoxovanadate Clusters
Understanding structure-property relationships is foundational to numerous modern chemistries, such as proton-coupled electron transfer (PCET). However, an experimentally measured property is the result of the behavior from an ensemble of molecules. Neglecting ensemble effects, especially under complex chemical environments, may obfuscate these relationships and lead to discrepancies between theory and experiment. In this work, we demonstrate the impact of configurational entropy and local chemical environments on hydroxide bond dissociation free energies [BDFE- (O−H)] for a set of polyoxovanadate nanoclusters, at ambient conditions. The O−H bond strengths are investigated via density functional theory (DFT) coupled with statistical thermodynamic analysis and bilinear modeling, and compared with previous experimental results on the same systems, namely electrochemical solutions of: [V 6 O 13−x (OH) x (TRIOL R ) 2 ] −2 (x = 2, 4, 6; R = NO 2 , Me) and [V 6 O 11−x (OMe) 2 (OH) x (TRIOL NO 2 ) 2 ] −2 (x = 2, 4). Interestingly, we find that ensemble effects, even at room temperature, can account for a significant portion of the BDFE(O−H) trend with the degree of reduction via H atom binding, which cannot be fully captured by single-structure, static DFT calculations. Moreover, we find that the ensemble effects may be replicated statistically, requiring only enumeration of energetically accessible H-binding sites. With the ensemble effects resolved, we present a simple bilinear model to reconcile remaining biases between experiment and ensemble-informed theory, which corelate with clusterspecific electronic environment differences. The bilinear model achieves outstanding accuracy vs experiments with a root-mean squared error of 0.4 kcal/mol. Finally, based on the physicochemical characteristics of hydrogen interaction with polyoxometalates, we present a simple methodology that captures the BDFE(O−H) trend while dramatically reducing required DFT calculations by 98% and achieving accuracy within 1 kcal/mol. Overall, this work elucidates the roles and structural origins of configurational entropy and chemical effects on polyoxometalate hydroxide bond energies, with potential applicability to various atomically precise metal oxide systems. Importantly, it introduces models for rapid and highly accurate property calculations in connection with experiments.
Cluster chemistry↗
Understanding and Predicting the Spatially Resolved Adsorption Properties of Nanoporous Materials
Using knowledge from statistical thermodynamics and crystallography, we develop an image–image translation model, called SorbIIT, that uses three-dimensional grids of adsorbate–adsorbent interaction energies as input to predict the spatially resolved loading surface of nanoporous materials over a broad range of temperatures and pressures. SorbIIT consists of a closed-form differential model for loading-surface prediction and a U-Net to generate spatial differential distributions from the energy grids. SorbIIT is trained using the energy grids and adsorbate distributions (obtained from high-throughput simulations) of 50 synthesized and 70 hypothetical zeolites and applied for predicting the adsorption of carbon dioxide, hydrogen sulfide, n-butane, 2-methylpropane, krypton, and xenon in other zeolites from 256 to 400 K. In conclusion, employing a quadratic isotherm model for the local differentiation, SorbIIT yields mean R 2 values of 0.998 for total adsorption and 0.6904 for local adsorption with a resolution of 0.2 Å, and a value of 0.721 for the structural similarity of the local loading distribution.
Sun, Yangzesheng [Univ. of Minnesota, Minneapolis,↗
CIGS Technology Advancement via Fundamental Modeling of Defect/Impurity Interactions (Final Technical Report)
The primary goals of the proposed work were to provide modeling tools (and the associated insight which comes along with model development) for design and optimization of CuIn x Ga 1-x Se 2 (CIGS) and CdSeTe (CST) solar cell manufacturing processes and to establish the foundation for comprehensive end-to-end predictive modeling tools to enable optimization of thin film photovoltaic technology for performance, cost, yield, and reliability. The initial focus of efforts within this project was to develop coupled process/optical/device models for CIGS PV technology and to work with Siva Power to apply that TCAD (technology computer-aided design) system to improve the efficiency and reduce manufacturing costs for CIGS solar cells. Our approach to that end was to generate an extensive database of DFT calculations and to use those calculations via statistical thermodynamics methods and Monte Carlo simulation to develop and characterize models for the behavior of native defects as well as intentional and unintentional impurities, including the redistribution of the primary components of CIGS films. Increased effort went toward coupling those models for defect behavior and composition evolution to the performance of multicrystalline CIGS solar cells via prediction of doping level and recombination lifetime as function of manufacturing process. In the second budget period, the project pivoted to developing a similar system for the CdSeTe system, focused especially on understanding the role of Se/Te alloy concentration. Execution of the project resulted in the successful development of TCAD systems for both CIGS and CdSeTe thin film PV within the Synopsys Sentaurus framework by utilizing the Alagator interface. In the first budget period of the project, we developed quantitative models for the major components of CIGS PV and implemented them within a framework that couples process, optical, and device simulation. From the insights we have gained, we identified novel opportunities for enhancing CIGS solar cell performance and have laid the groundwork to further optimize the layer structure, composition profile, and thermal cycles for substantially improved efficiency and lower manufacturing costs. For the CIGS system, process changes to achieve greater than 1% absolute enhancement in efficiency were identified, but testing of those approaches was stymied by lack of a domestic CIGS manufacturing partner after the closure of Siva Power as well as Miasole. For CdSeTe, a fully capable TCAD system only became ready to apply near the end of the project period, so substantial opportunities remain to apply those models to enhance the leading thin film PV technology.
14 SOLAR ENERGY↗