Showing papers on "Gibbs–Duhem equation published in 2005"

Thermodynamics of two-dimensional single-component elastic crystalline solids: single-wall carbon nanotubes

Abstract: The thermodynamic behaviour of two-dimensional single-component elastic crystalline solids is developed: the surface Euler's equation, the surface Gibbs equation, the surface Gibbs–Duhem equation, and the conditions to be expected at equilibrium, including the stress-deformation behaviour of the crystal. The analysis recognizes that the surface Helmholtz free energy is an explicit function of the lattice vectors defining the crystalline structure. As an application, we obtain the stress-deformation behaviour of single-wall carbon nanotubes which are composed of a regular two-dimensional array of hexagonal lattices of carbon atoms. Using two potentials, Tersoff [1]–Brenner [2] and Brenner et al. [3] to describe interatomic potentials and hence the specific surface Helmholtz free energy, we compute the surface elastic properties for the single-wall carbon nanotubes. These are compared with the available experimental values.

Euclidean Gibbs Measures of Quantum Anharmonic Crystals

Abstract: A lattice system of interacting temperature loops, which is used in the Euclidean approach to describe equilibrium thermodynamic properties of an infinite system of interacting quantum particles performing anharmonic oscillations (quantum anharmonic crystal), is considered. For this system, it is proven that: (a) the set of tempered Gibbs measures is non-void and weakly compact; (b) every Gibbs measure obeys an exponential integrability estimate, the same for all such measures; (c) every Gibbs measure has a Lebowitz-Presutti type support; (d) the set of all Gibbs measures is a singleton at high temperatures. In the case of attractive interaction and one-dimensional oscillations we prove that at low temperatures the system undergoes a phase transition. The uniqueness of Gibbs measures due to strong quantum effects (strong diffusivity) and at a nonzero external field are also proven in this case. Thereby, a complete description of the properties of the set of all Gibbs measures has been done, which essentially extends and refines the results obtained so far for models of this type.

On the geometrical thermodynamics of chemical reactions

Abstract: The formal structure of geometrical thermodynamics is reviewed with particular emphasis on the geometry of equilibria submanifolds. On these submanifolds thermodynamic metrics are defined as the Hessian of thermodynamic potentials. Links between geometry and thermodynamics are explored for single and multiple component, closed and open systems. For multi-component closed and open systems the Gibbs free energy is employed as the thermodynamic potential to investigate the connection between geometry and thermodynamics. The Gibbs free energy is chosen for the analysis of multicomponent systems and, in particular, chemical reactions.

Time-Averages and the Heat Theorem

Abstract: In this paper it is illustrated how to compute the time–average of a generic dynamical variable in the limit of large systems. It is also shown how to use this result to deduce an analogue of the second principle of thermodynamics, even in presence of metastable phenomena, for which it is not granted that the standard Gibbs measure can be used.

Equivalent gibbs duhem law in network queue

Abstract: High speed networks are highly dynamical systems. Large deviation techniques have been employed to characterize their loss probability. Large deviation is also used to calculate shadow prices of quality of service of a scalable network queue with respect to buffer size B, capacity C and arrival rate N.In this paper we prove that these shadow prices are independent of (B,C,N) parameters. Gibbs Duhem law of thermodynamics is described. Equivalent Gibbs Duhem type law in scalable network queue is derived. Application of equivalent network Gibbs Duhem law is discussed.