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PubMed1988

Thermodynamics of cosmological matter creation.

A type of cosmological history that includes large-scale entropy production is proposed. These cosmologies are based on reinterpretation of the matter-energy stress tensor in Einstein's equations. This modifies the usual adiabatic energy conservation laws, thereby including irreversible matter creation. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. This point of view results from consideration of the thermodynamics of open systems in the framework of cosmology. It is shown that the second law of thermodynamics requires that space-time transforms into matter, while the inverse transformation is forbidden. It appears that the usual initial singularity associated with the big bang is structurally unstable with respect to irreversible matter creation. The corresponding cosmological history therefore starts from an instability of the vacuum rather than from a singularity. This is exemplified in the framework of a simple phenomenological model that leads to a three-stage cosmology: the first drives the cosmological system from the initial instability to a de Sitter regime, and the last connects with the usual matter-radiation Robertson-Walker universe. Matter as well as entropy creation occurs during the first two stages, while the third involves the traditional cosmological evolution. A remarkable fact is that the de Sitter stage appears to be an attractor independent of the initial fluctuation. This is also the case for all the physical predictions involving the present Robertson-Walker universe. Most results obtained previously, in the framework of quantum field theory, can now be obtained on a macroscopic basis. It is shown that this description leads quite naturally to the introduction of primeval black holes as the intermediate stage between the Minkowski vacuum and the present matter-radiation universe. The instability at the origin of the universe is the result of fluctuations of the vacuum in which black holes act as membranes that stabilize these fluctuations. In short, black holes will be produced by and "inverse" Hawking radiation process and, once formed, will decompose into "real" matter through the usual Hawking radiation. In this way, the irreversible transformation of space-time into matter can be described as a phase separation between matter and gravitation in which black holes play the role of "critical nuclei."

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PubMed1991

Global and local metric geometry of ligand binding thermodynamics.

An abstract metric representation of ligand binding thermodynamics reveals the basic connections between the classical thermodynamic theory of binding and linkage [Wyman, J. (1964) Adv. Protein Chem. 19, 223-286] and its site-specific formulation [Di Cera, E. (1990) Biophys. Chem. 37, 147-164]. These two approaches are limit cases of a general metric formulation of binding and linkage that also includes a number of intermediate "mixed" representations.

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PubMed2002

Mathematical models of solute retention in gas chromatography as sources of thermodynamic data. Part 1. Methyl n-alkyl ketones as the test analytes.

Although gas chromatography (GC) is mainly used for analytical and preparative separation of complicated mixtures and then identification of the separated components, it can also be used as a relatively simple tool for the determination of physicochemical (including thermodynamic) properties. In this study, we discuss three different retention models devised specially for GC. They are tested for a homologous series of methyl n-alkyl ketones chromatographed on stationary phases of low and medium polarity at several different isothermal temperatures. The statistical performance of each model is excellent, which makes them a convenient tool for the evaluation of analyte retention under the given working conditions. They can also be used for the determination of the numerical values of thermodynamic properties (e.g., the enthalpy of vaporization of the analytes and the standard molar chemical potential of the partitioning of one methylene group (-CH2-) between the stationary and mobile phases).

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PubMed1991

A thermodynamic study of unusually stable RNA and DNA hairpins.

About 70% of the RNA tetra-loop sequences identified in ribosomal RNAs from different organisms fall into either (UNCG) or (GNRA) families (where N = A, C, G, or U; and R = A or G). RNA hairpins with these loop sequences form unusually stable tetra-loop structures. We have studied the RNA hairpin GGAC(UUCG)GUCC and several sequence variants to determine the effect of changing the loop sequence and the loop-closing base pair on the thermodynamic stability of (UNCG) tetra-loops. The hairpin GGAG(CUUG)CUCC with the conserved loop G(CUUG)C was also unusually stable. We have determined melting temperatures (Tm), and obtained thermodynamic parameters for DNA hairpins with sequences analogous to stable RNA hairpins with (UNCG), C(GNRA)G, C(GAUA)G, and G(CUUG)C loops. DNA hairpins with (TTCG), (dUdUCG), and related sequences in the loop, unlike their RNA counterparts, did not form unusually stable hairpins. However, DNA hairpins with the consensus loop sequence C(GNRA)G were very stable compared to hairpins with C(TTTT)G or C(AAAA)G loops. The C(GATA)G and G(CTTG)C loops were also extra stable. The relative stabilities of the unusually stable DNA hairpins are similar to those observed for their RNA analogs.

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PubMed1992

Predicting antisense oligonucleotide inhibitory efficacy: a computational approach using histograms and thermodynamic indices.

Antisense oligonucleotides (ASOs) are designed to bind to a specific mRNA and selectively suppress its translation. To facilitate selection of optimal ASO targets, we have developed three thermodynamic indices to evaluate putative structural complexes important in ASO action. These indices are: a secondary structure score (Sscore), which estimates the strength of local mRNA secondary structures at the ASO target site; a duplex score (Dscore), which estimates the delta Gformation for the ASO:mRNA target sequence duplex; and a competition score (Cscore), which is the difference between the Dscore and the Sscore. We also present two histograms to graphically display these indices from different regions of the mRNA. The indices are compared to the inhibition reported in five studies of ASO-mediated suppression of gene expression. The Dscore is the most consistent predictor of ASO efficacy in four of the five studies (r2 from 0.44 to 0.99), while the results of the fifth study could not be predicted by any thermodynamic or physical index. Thus the Dscores and their histogram may prove useful in selection of ASO targets.

Algorithms↗
PubMed2005

Thermodynamic conditions for stability in materials with rate-independent dissipation.

A distinctive feature of the examined class of solids is that a part of the entropy production is due to rate-independent dissipation, as in models of plasticity, damage or martensitic transformations. The standard condition for thermodynamic stability is shown to be too restrictive for such solids and, therefore, an extended condition for stability of equilibrium is developed. The classical thermodynamic theory of irreversible processes is used along with the internal variable approach, with the emphasis on the macroscopic effects of micro-scale instabilities in the presence of two different scales of time. Specific conditions for material stability against internal structural rearrangements under deformation-sensitive loading are derived within the incremental constitutive framework of multi-mode inelasticity. Application to spontaneous formation of deformation bands in a continuum is presented. Conditions for stability or instability of a quasi-static process induced by varying loading are given under additional constitutive postulates of normality and symmetry. As illustration of the theory, the stability of equilibrium or a deformation path under uniaxial tension is analysed for a class of inelastic constitutive laws for a metal crystal deformed plastically by multi-slip or undergoing stress-induced martensitic transformation.

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PubMed1999

Thermodynamic perturbation theory for polydisperse colloidal suspensions using orthogonal polynomial expansions.

We present a method for calculating the thermodynamic and structural properties of a polydisperse liquid by means of a thermodynamic perturbation theory: the optimized random phase approximation (ORPA). The approach is an extension of a method proposed recently by one of us for an integral equation application [Phys. Rev. E 54, 4411 (1996)]. The method is based on expansions of all sigma-dependent functions in the orthogonal polynomials p(i)(sigma) associated with the weight function f(Sigma)(sigma), where sigma is a random variable (in our case the size of the particles) with distribution f(Sigma)(sigma). As in the one-component or general N-component case, one can show that the solution of the ORPA is equivalent to the minimization of a suitably chosen functional with respect to variations of the direct correlation functions. To illustrate the method, we study a polydisperse system of square-well particles; extension to other hard-core or soft-core systems is straightforward.

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PubMed1999

Ergodic properties of a generic nonintegrable quantum many-body system in the thermodynamic limit.

We study a generic but simple nonintegrable quantum many-body system of locally interacting particles, namely, a kicked-parameter (t,V) model of spinless fermions on a one-dimensional lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2 spins). The statistical properties of the dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in the thermodynamic limit are considered as the kick parameters (which control the degree of nonintegrability) are varied. We find and demonstrate ballistic transport and nonergodic, nonmixing dynamics (implying infinite conductivity at all temperatures) in the integrable regime of zero or very small kick parameters, and more generally and importantly, also in the nonintegrable regime of intermediate values of kicked parameters, whereas only for sufficiently large kick parameters do we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness D) which controls the phase transition from nonmixing and nonergodic dynamics (ordered phase, D>0) to mixing and ergodic dynamics (disordered phase, D=0) in the thermodynamic limit. Furthermore, we find exponential decay of time correlation functions in the regime of mixing dynamics. The results are obtained consistently within three different numerical and analytical approaches: (i) time evolution of a finite system and direct computation of time correlation functions, (ii) full diagonalization of finite systems and statistical analysis of stationary data, and (iii) algebraic construction of quantum invariants of motion of an infinite system, in particular the time-averaged observables.

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PubMed1999

Thermodynamically self-consistent theories of fluids interacting through short-range forces.

The self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths lambda, ranging from lambda=1.8 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda=9 (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low lambda's all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At lambda=4 some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest lambda values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher lambda's the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase "freezing criterion" (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC; the GMSA prediction for the freezing line at lambda=7 and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified.

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PubMed1999

Thermodynamic basis for a variational model for crystal growth.

Variational models provide an alternative approach to standard sharp interface models for calculating the motion of phase boundaries during solidification. We present a correspondence between objective functions used in variational simulations and specific thermodynamic functions. We demonstrate that variational models with the proposed identification of variables are consistent with nonequilibrium thermodynamics. Variational models are derived for solidification of a pure material and then generalized to obtain a model for solidification of a binary alloy. Conservation laws for internal energy and chemical species and the law of local entropy production are expressed in integral form and used to develop variational principles in which a "free energy," which includes an interfacial contribution, is shown to be a decreasing function of time. This free energy takes on its minimum value over any short time interval, subject to the laws of conservation of internal energy and chemical species. A variational simulation based on this model is described, and shown for small time intervals to provide the Gibbs-Thomson boundary condition at the solid-liquid interface.

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PubMed2000

Diffusion-limited aggregation: A relationship between surface thermodynamics and crystal morphology

We have combined the original diffusion-limited aggregation model introduced by Witten and Sander with the surface thermodynamics of the growing solid aggregate. The theory is based on the consideration of the surface chemical potential as a thermodynamic function of the temperature and nearest-neighbor configuration. The Monte Carlo simulations on a two-dimensional square lattice produce the broad range of shapes such as fractal dendritic structures, densely branching patterns, and compact aggregates. The morphology diagram illustrating the relationship between the model parameters and cluster geometry is presented and discussed.

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PubMed2000

Thermodynamic picture of the glassy state gained from exactly solvable models

A picture for thermodynamics of the glassy state was introduced recently by us [Phys. Rev. Lett. 79, 1317 (1997); 80, 5580 (1998)]. It starts by assuming that one extra parameter, the effective temperature, is needed to describe the glassy state. This approach connects responses of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized, nonequilibrium way. Similar universal relations do not hold between energy fluctuations and the specific heat. In the present paper, the underlying arguments are discussed in greater length. The main part of the paper involves details of the exact dynamical solution of two simple models introduced recently: uncoupled harmonic oscillators subject to parallel Monte Carlo dynamics, and independent spherical spins in a random field with such dynamics. At low temperature, the relaxation time of both models diverges as an Arrhenius law, which causes glassy behavior in typical situations. In the glassy regime, we are able to verify the above-mentioned relations for the thermodynamics of the glassy state. In the course of the analysis, it is argued that stretched exponential behavior is not a fundamental property of the glassy state, though it may be useful for fitting in a limited parameter regime.

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PubMed2000

Structure and thermodynamic properties of a binary liquid in a porous matrix: the formalism

Using the replica trick we derive a formalism to describe the structure and the thermodynamic properties of a binary liquid in equilibrium with a porous medium. We present the replica Ornstein-Zernike equations for the general case of a k-component liquid inside a porous matrix; besides the usual liquid-state closure relations, we consider in particular the optimized random phase approximation (ORPA) restricting ourselves at present to hard-core potentials exclusively. We present furthermore several thermodynamic relations: the Gibbs-Duhem equation, the compressibility, and the viral equation. Within the framework of the ORPA (mean spherical approximation), closed expressions for the perturbation contribution to the free energy and the chemical potentials can be presented. Finally, we offer suggestions for numerical implementations.

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PubMed2000

Levy diffusion in a force field, huber relaxation kinetics, and nonequilibrium thermodynamics: H theorem for enhanced diffusion with Levy white noise

A characteristic functional approach is suggested for Levy diffusion in disordered systems with external force fields. We study the overdamped motion of an ensemble of independent particles and assume that the force acting upon one particle is made up of two additive components: a linear term generated by a harmonic potential and a second term generated by the interaction with the disordered system. The stochastic properties of the second term are evaluated by using Huber's approach to complex relaxation [Phys. Rev. B 31, 6070 (1985)]. We assume that the interaction between a moving particle and the environment can be expressed by the contribution of a large number of relaxation channels, each channel having a very small probability of being open and obeying Poisson statistics. Two types of processes are investigated: (a) Levy diffusion with static disorder for which the fluctuations of the random force are frozen and last forever and (b) diffusion with strong dynamic disorder and independent Levy fluctuations (Levy white noise). In both cases we show that the probability distribution of the position of a diffusing particle tends towards a stationary nonequilibrium form. The characteristic functional of concentration fluctuations is evaluated in both cases by using the theory of random point processes. For large times the fluctuations of the concentration field are stationary and the corresponding probability density functional can be evaluated analytically. In this limit the fluctuations depend on the distribution of the total number of particles but are independent of the initial positions of the particles. We show that the logarithm of the stationary probability functional plays the role of a nonequilibrium thermodynamic potential, which has a structure similar to the Helmholtz free energy in equilibrium thermodynamics: it is made up of the sum of an energetic component, depending on the external mechanical potential, and of an entropic component, depending on the concentration field. We show that the conditions for the existence and stability of the nonequilibrium steady state, which emerges for large times, can be expressed in terms of the stochastic potential. For Levy white noise the average concentration field can be expressed as the solution of a fractional Fokker-Planck equation. We show that the stochastic potential is a Lyapunov function of the fractional Fokker-Planck equation, which ensures that all transient solutions for the average concentration field tend towards a unique stationary form.

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PubMed2000

Maximal work problem in finite-time thermodynamics

In this paper three problems are considered: (a) the maximal work that can be produced in a finite time in a thermodynamic system; (b) the minimal work which must be done in order to transform an equilibrium thermodynamic system into a number of subsystems that are out of equilibrium with each other in finite time; and (c) the maximal power that can be achieved in a finite time. The mathematical features of these problems are investigated. It is shown that in many cases the limiting work processes here are processes where intensive variables are piecewise-constant functions of time, and that these functions take not more than some predefined number of values. It is demonstrated that many results obtained for a number of particular systems (heat engines, heat transfer) follow from the general conditions for limiting processes derived in this paper. Conditions for limiting work regimes in mass transfer processes are obtained.

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PubMed2000

Towards the thermodynamics of localization processes

We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger [Phys. Rev. Lett. 82, 520 (1999)] found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear-in-time regime of entropy increase, that is, a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the nonextensive entropic indicator advocated by Tsallis [J. Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that the adoption of the "magic" value q=Q=1/2, compared to the traditional entropic index q=1, reduces the length of the transient regime and makes earlier the emergence of the Kolmogorov regime. We adopt a two-site model to explain these properties by means of an analytical treatment and we argue that Q=1/2 might be a typical signature of the occurrence of Anderson localization.

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PubMed2000

Multibaker map for thermodynamic cross effects in dynamical systems

A consistent description of simultaneous heat and particle transport, including cross effects, and the associated entropy balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where, in addition to the phase-space density of the multibaker, a second field with appropriate source terms is included in order to mimic a spatial temperature distribution and its time evolution. Conditions are given to ensure consistency in an appropriately defined continuum limit with the thermodynamic entropy balance. They leave as the only free parameter of the model the entropy flux let directly into the surroundings. If it vanishes in the bulk, the transport properties of the model are described by the thermodynamic transport equations. Another choice leads to a uniform temperature distribution. It represents transport problems treated by means of a thermostating algorithm, similar to the one considered in nonequilibrium molecular dynamics.

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PubMed2000

Effects of dispersion forces on the structure and thermodynamics of fluid krypton

Semianalytical and numerical calculations are performed to predict the structural and thermodynamic properties of low-density Kr fluid. Assuming that the interatomic forces can be modelled by a pairwise potential plus the three-body Axilrod-Teller potential, two different routes are explored. The first one is based on the hybridized mean spherical approximation integral equation of the theory of liquids and the second one uses large-scale molecular dynamics (MD). Algorithms for MD simulation are constructed on parallel machines to reduce the amount of computer time induced by the calculations of the three-body forces and the pair-correlation function. Our results obtained with the two methods mentioned above are in quite good agreement with the recent small-angle neutron-scattering experiments [Formisano et al., Phys. Rev. Lett. 79, 221 (1997); Benmore et al., J. Phys.: Condens. Matter 11, 3091 (1999)]. Moreover, the reliability of the asymptotic form of the integral equation is assessed for the specific case of dispersion forces including the three-body contributions, by an analysis at low wave vector and low density. It is seen that the effects of the Axilrod-Teller triple-dipole potential cannot be ignored to describe the structure and the thermodynamic properties of fluid krypton even at low density.

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