Thermodynamical Interpretation Research Articles

Robust Exponential Acceleration in Time-Dependent Billiards

A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growth rate is found analytically and is, thus, controllable. Numerical simulations corroborate the analytic predictions with good precision. The acceleration mechanism has a natural thermodynamical interpretation and is applied to a hot dilute gas of repelling particles.

THERMODYNAMICS OF INTERACTING ENTROPY-CORRECTED HOLOGRAPHIC DARK ENERGY IN A NON-FLAT FRW UNIVERSE

An entropy-corrected holographic dark energy (ECHDE) was recently proposed to explain the dark energy-dominated universe with the help of quantum corrections to the entropy–area relation in the setup of loop quantum cosmology. Using this new definition, we investigate its thermodynamical features including entropy and energy conservation. We describe the thermodynamical interpretation of the interaction between ECHDE and dark matter in a non-flat universe. We obtain a relation between the interaction term of the dark components and thermal fluctuation. Our study further generalizes the earlier works86, 87 in this direction.

GENERALIZED SECOND LAW OF THERMODYNAMICS IN WARPED DGP BRANEWORLD

We investigate the validity of the generalized second law of thermodynamics on the (n - 1)-dimensional brane embedded in the (n + 1)-dimensional bulk. We examine the evolution of the apparent horizon entropy extracted through relation between gravitational equation and the first law of thermodynamics together with the matter field entropy inside the apparent horizon. We find that the apparent horizon entropy extracted through connection between gravity and the first law of thermodynamics satisfies the generalized second law of thermodynamics. This result holds regardless of whether there is the intrinsic curvature term on the brane or a cosmological constant in the bulk. The observed satisfaction of the generalized second law provides further support on the thermodynamical interpretation of gravity based on the profound connection between gravity and thermodynamics.

Computation of Current Cumulants for Small Nonequilibrium Systems

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrödinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.

Thermodynamical interpretation of the interacting holographic dark energy model in a non-flat universe

Motivated by the recent work of Wang, Lin, Pavon, and Abdalla [B. Wang, C.Y. Lin, D. Pavon, E. Abdalla, Phys. Lett. B 662 (2008) 1, arXiv: 0711.2214 [hep-th]], we generalize their work to the non-flat case. In particular, we provide a thermodynamical interpretation for the holographic dark energy model in a non-flat universe. For this case, the characteristic length is no more the radius of the event horizon (RE) but the event horizon radius as measured from the sphere of the horizon (L). Furthermore, when interaction between the dark components of the holographic dark energy model in the non-flat universe is present its thermodynamical interpretation changes by a stable thermal fluctuation. A relation between the interaction term of the dark components and this thermal fluctuation is obtained. In the limiting case of a flat universe, i.e. k=0, all results given in [B. Wang, C.Y. Lin, D. Pavon, E. Abdalla, Phys. Lett. B 662 (2008) 1, arXiv: 0711.2214 [hep-th]] are obtained.

A measure of de Sitter entropy and eternal inflation

We show that in any model of non-eternal inflation satisfying the null energy condition, the area of the de Sitter horizon increases by at least one Planck unit in each inflationary e-folding. This observation gives an operational meaning to the finiteness of the entropy S_dS of an inflationary de Sitter space eventually exiting into an asymptotically flat region: the asymptotic observer is never able to measure more than e^(S_dS) independent inflationary modes. This suggests a limitation on the amount of de Sitter space outside the horizon that can be consistently described at the semiclassical level, fitting well with other examples of the breakdown of locality in quantum gravity, such as in black hole evaporation. The bound does not hold in models of inflation that violate the null energy condition, such as ghost inflation. This strengthens the case for the thermodynamical interpretation of the bound as conventional black hole thermodynamics also fails in these models, strongly suggesting that these theories are incompatible with basic gravitational principles.

Investigation of the enhanced solubility of fluorinated methanes in CO 2 by Monte Carlo simulation: Absolute free energy of solvation and structural properties of solution

The absolute free energy of solvation of methane (CH 4) and its fluorinated forms (CH 3F, CH 2F 2, CHF 3 and CF 4) have been computed via statistical perturbation theory (SPT) in the NPT ensemble at four thermodynamical states (whitin liquid and supercritical regions), in the context of Monte Carlo Simulations. Thermodynamical interpretation of the observed trend in the absolute free energy of solvation in different states reveals an exothermic solvation with Δ S slv < 0 (entropically unfavorable solvation) that the intermolecular interactions play an important role in the solvation process. The fluorinated methanes are confirmed to control the mutual arrangement of neighboring CO 2 molecules and the axis of CO 2 molecules near F atom of fluorinated solutes make a right angle with F(solute)–C(CO 2) axis. Moreover, the energetic distribution along with structural and orientational distributions confirm the existence of a direct interaction between CO 2 and F atom, although the extent of this interaction is not very large.

Thermodynamical analysis of the shape and size dispersion ofInAs∕InP(001)quantum dots

We give a thermodynamical interpretation of the size and shape dispersion of $\mathrm{In}\mathrm{As}∕\mathrm{In}\mathrm{P}(001)$ quantum dots (QD's) grown by metalorganic vapor phase epitaxy. A careful determination of the QD geometry is performed by analyzing transmission electron microscopy images. QD's are parallelogram shaped, with edges slightly elongated along the [1-30] and [3-10] directions. The analytical model of Tersoff et al. is adapted to our QD geometry to determine the amount of elastic energy relaxed during the QD formation. A comparison between experiments and calculations shows that QD elongation becomes favorable when the volume of QD's exceeds a critical value, which is determined experimentally and theoretically with quantitatively good agreement. QD anisotropy is shown to be strongly dependent on the excess of material provided on the growth surface after they have reached their critical volume.

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor, II

In our previous report [Aita, T., Morinaga, S., Hosimi, Y., 2004. Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor I. Bull. Math. Biol. 66, 1371–1403], an analogy between thermodynamics and adaptive walks on a Mt. Fuji-type fitness landscape in an artificial selection system was presented. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrated that the adaptive walk (=evolution) is driven by the evolutionary force in the direction in which free fitness increases. In this report, we examine the effect of various modifications of the original model on the properties of the adaptive walk. The modifications were as follows: first, mutation distance d was distributed obeying binomial distribution; second, the selection process obeyed the natural selection protocol; third, ruggedness was introduced to the landscape according to the NK model; fourth, a noise was included in the fitness measurement. The effect of each modification was described in the same theoretical framework as the original model by introducing ‘effective’ quantities such as the effective mutation distance or the effective screening size.

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in a evolution reactor, I

A theory for describing evolution as adaptive walks by a finite population with M walkers ( M≥1) on an anisotropic Mt. Fuji-type fitness landscape is presented, from a thermodynamical point of view. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrate that the behavior of these theoretical walkers is almost consistent with the thermodynamical schemes. The major conclusions are as follows: (1) an adaptive walk (=evolution) is driven by an evolutionary force in the direction in which free fitness increases; (2) the expectation of the climbing rate obeys an equation analogous to the Einstein relation in Brownian motion; (3) the standard deviation of the climbing rate is a quantity analogous to the mean thermal energy of a particle, kT(×constant). In addition, on the interpretation that the walkers climb the landscape by absorbing ‘fitness information’ from the surroundings, we succeeded in quantifying the fitness information and formulating a macroscopic scheme from an informational point of view.

Thermodynamical interpretation of an adaptive walk on a Mt. Fuji-type fitness landscape: Einstein relation-like formula holds in a stochastic evolution

We have theoretically studied the statistical properties of adaptive walks (or hill-climbing) on a Mt. Fuji-type fitness landscape in the multi-dimensional sequence space through mathematical analysis and computer simulation. The adaptive walk is characterized by the “mutation distance” d as the step-width of the walker and the “population size” N as the number of randomly generated d-fold point mutants to be screened. In addition to the fitness W, we introduced the following quantities analogous to thermodynamical concepts: “free fitness” G( W)≡ W+ T× S( W), where T is the “evolutionary temperature” T∝ d/ ln N and S( W) is the entropy as a function of W, and the “evolutionary force” X≡d( G( W)/ T)/d W, that is caused by the mutation and selection pressure. It is known that a single adaptive walker rapidly climbs on the fitness landscape up to the stationary state where a “mutation–selection–random drift balance” is kept. In our interpretation, the walker tends to the maximal free fitness state, driven by the evolutionary force X. Our major findings are as follows: First, near the stationary point W ∗ , the “climbing rate” J as the expected fitness change per generation is described by J≈ L× X with L≈ V/2, where V is the variance of fitness distribution on a local landscape. This simple relationship is analogous to the well-known Einstein relation in Brownian motion. Second, the “biological information gain” (Δ G/ T) through adaptive walk can be described by combining the Shannon's information gain (Δ S) and the “fitness information gain” (Δ W/ T).

配列空間に於ける実験室内分子進化ダイナミクスの熱力学的概念による解釈

配列空間に於ける実験室内分子進化ダイナミクスの熱力学的概念による解釈

Calcium-binding parameter of Bacillus amyloliquefaciens alpha-amylase determined by inactivation kinetics.

The irreversible thermal inactivation and the thermodynamics of calcium ion binding of Bacillus amyloliquefaciens alpha-amylase in the absence of substrates were studied. The enzyme inactivation on heating was apparently followed by first-order kinetics. The enzyme was stabilized with an increased concentration of calcium ion and thus the inactivation was highly dependent on the state of calcium binding. The activation parameter for the inactivation suggests an unfolding of the enzyme protein upon heating. Values of both the activation enthalpy and entropy were increased with a higher calcium ion concentration. An inactivation kinetic model is based on the assumption of a two-stage unfolding transition in which the bivalent ion dissociation occurs in the first step followed by the secondary structural unfolding. This simple kinetic model provides both a qualitative and quantitative interpretation of calcium ion binding to the enzyme and its effect on the inactivation properties. The specific approximations of the kinetic model were strictly followed in the analysis to calculate the apparent inactivation rate at each calcium ion concentration in terms of the calcium-binding parameters. The enthalpy and entropy changes for the calcium ion binding were calculated to be -149 kJ/mol and -360 J.mol(-1).K(-1) respectively and these values suggest a strong enthalpic affinity for the bivalent ion binding to the enzyme protein. The thermodynamical interpretation attempts to provide clear relations between the terms of an apparent inactivation rate and the calcium binding.

Thermodynamic Interpretation of the Quantum Error Correcting Criterion

Shannon's fundamental coding theorems relate classical information theory to thermodynamics. More recent theoretical work has been successful in relating quantum information theory to thermodynamics. For example, Schumacher proved a quantum version of Shannon's 1948 classical noiseless coding theorem. In this note, we extend the connection between quantum information theory and thermodynamics to include quantum error correction. There is a standard mechanism for describing errors that may occur during the transmission, storage, and manipulation of quantum information. One can formulate a criterion of necessary and sufficient conditions for the errors to be detectable and correctable. We show that this criterion has a thermodynamical interpretation. PACS: 03.67; 05.30; 63.10

Thermodynamical interpretation of the variational Maxwell theorem in dc circuits

We point out a thermodynamic interpretation of the variational Maxwell theorem relative to dc circuits, based on the minimum of the entropy production. We thus complete the interesting pedagogical analysis of D. A. Van Baak in a recent paper concerning the use of variational methods on dc circuits.

Consequence of structural identifiability properties on state-model formulation for linear inverse chromatography

In this paper, a study concerning the problem of parameter estimation from one-component chromatographic experiments when linear models can be adopted is presented. The question is to know exactly which parameters can be theoretically estimated from an experiment when time-domain analysis is used. This question is independent of the measurement noise and depends only on the structure of the model used for the estimation procedure. To illustrate the approach, the identifiability concept is used here in the case of two examples of linear models: the N CSTRSs in series model and the plug flow with axial dispersion model. In the first case, the adsorbant concentration is supposed to be uniform, leading to a lumped parameter model. In the second case, Fickian diffusion is taken into account in the solid, leading to a distributed parameter model. The transfer function approach is used to test the parameter identifiability. A change of state variable is proposed in order to formulate the state-models according to a form suited to the parameter estimation purpose. This analysis is numerically illustrated in the case of the second model by using the data of Hufton and Danner, A.I.Ch.E. Journal, 39(6) (1993) 962–974, 954–961. A thermodynamical interpretation of the result is also given.

The role of backstress in phase transforming steels

Transformation Induced Plasticity (TRIP) is demonstrated by an experimental programme for a Fe-9Ni-12Cr steel for various loading paths with partial or full unloading. The martensitic transformation is considered. A thermodynamical interpretation as well as micromechanical modelling of TRIP are presented. The selection of distinct variants is explained. Finally a modified constitutive equation for the TRIP strain rate is suggested by introducing a transformation surface including a transformation backstress. The backflow after unloading, which cannot be explained by the currently used TRIP strain rate term, can be represented by the proposed formulation. Aspects of future research are discussed.

Holography and Riemann surfaces

We study holography for asymptotically AdS spaces with an arbitrary genus compact Riemann surface as the conformal boundary. Such spaces can be constructed from the Euclidean AdS_3 by discrete identifications: the discrete groups one uses are the so-called classical Schottky groups. As we show, the spaces so constructed have an appealing interpretation of ``analytic continuations'' of the known Lorentzian signature black hole solutions: it is one of the motivations for our generalization of the holography to this case. We use the semi-classical approximation to the gravity path integral, and calculate the gravitational action for each space, which is given by the (appropriately regularized) volume of the space. As we show, the regularized volume reproduces exactly the action of Liouville theory, as defined on arbitrary Riemann surfaces by Takhtajan and Zograf. Using the results as to the properties of this action, we discuss thermodynamics of the spaces and analyze the boundary CFT partition function. Some aspects of our construction, such as the thermodynamical interpretation of the Teichmuller (Schottky) spaces, may be of interest for mathematicians working on Teichmuller theory.

Ideal gas sources for the Lemaître-Tolman-Bondi metrics

New exact solutions emerge by replacing the dust source of the Lemaître-Tolman-Bondi metrics with a viscous fluid satisfying the monatomic gas equation of state. The solutions have a consistent thermodynamical interpretation. The most general transport equation of extended irreversible thermodynamics is satisfied, with phenomenological coefficients bearing a close resemblance to those characterizing a non-relativistic Maxwell-Boltzmann gas.

Relationships between rheological properties, morphological characteristics, and composition of bitumen-styrene butadiene styrene copolymers mixes. II. A thermodynamical interpretation

The variations of the dynamic mechanical properties (at 5 Hz) of bitumen–SBS mixes in the function of their composition (polymer content, bitumen composition) have been established. The relationships between the viscoelastic measurements and the morphological characteristics, previously determined, have been used to interprete these variations in terms of change of morphological characteristics (phase composition, phase content in the blends). Finally, a theoretical approach based on the thermodynamics of mixing is proposed to explain the relationships between the composition and the morphological characteristics. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:1609–1618, 1997