Journal of Statistical Physics 

About: Journal of Statistical Physics is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Ising model & Phase transition. It has an ISSN identifier of 0022-4715. Over the lifetime, 9964 publications have been published receiving 313920 citations.

Possible generalization of Boltzmann-Gibbs statistics

Abstract: With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS q ≡k [1 – ∑ i=1 W p i q ]/(q-1), whereq∈ℝ characterizes the generalization andp i are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.

Quantitative universality for a class of nonlinear transformations

Abstract: A large class of recursion relations xn+l = Af(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum 2. With f(2) - f(x) ~ Ix - 21" (for Ix - 21 sufficiently small), z > 1, the universal details depend only upon z. In particular, the local structure of high-order stability sets is shown to approach universality, rescaling in successive bifurcations, asymptotically by the ratio c~ (a = 2.5029078750957... for z = 2). This structure is determined by a universal function g*(x), where the 2"th iterate off, f("~, converges locally to ~-"g*(~nx) for large n. For ithe class of f's considered, there exists a A~ such that a 2"-point stable limit cycle including :7 exists; A~ - ~ ~ ~-" (~ = 4.669201609103... for z = 2). The numbers = and have been computationally determined for a range of z through their definitions, for a variety off's for each z. We present a recursive mechanism that explains these results by determining g* as the fixed-point (function) of a transformation on the class off's. At present our treatment is heuristic. In a sequel, an exact theory is formulated and specific problems of rigor isolated.

Optimization by Simulated Annealing: Quantitative Studies

Abstract: Simulated annealing is a stochastic optimization procedure which is widely applicable and has been found effective in several problems arising in computeraided circuit design. This paper derives the method in the context of traditional optimization heuristics and presents experimental studies of its computational efficiency when applied to graph partitioning and traveling salesman problems.

Fluids with highly directional attractive forces. I. Statistical thermodynamics

Abstract: A new formulation of statistical thermodynamics is derived for classical fluids of molecules that tend to associate into dimers and possibly highers-mers due to highly directional attraction. A breakup of the pair potential into repulsive and highly directionally attractive parts is introduced into the expansion of the logarithm of the grand partition function in fugacity graphs. The bonding by the directional attraction is used to classify the graphs and to introduce a topological reduction which results in the replacement of the fugacity by two variables: singlet densityρ and monomer densityρ 0. Results for the thermodynamic functions as functionals ofρ andρ 0 are given in the form of graph sums. Pair correlations are analyzed in terms of a new matrix analog of the direct correlation function. It is shown that the low-density limit is treated exactly, while major difficulties arise when the Mayer expansion, which employs onlyp, is used. The intricate resummations required for the Mayer expansion are illustrated for the case where dimers are the only association products.

The Theory of Ostwald Ripening

Abstract: Developments in the theory of Ostwald ripening since the classic work of I. M. Lifshitz and V. V. Slyozov (LS) are reviewed and directions for future work are suggested. Recent theoretical work on the role of a finite volume fraction of coarsening phase on the ripening behavior of two-phase systems is reformulated in terms of a consistent set of notation through which each of the theories can be compared and contrasted. Although more theoretical work is necessary, these theories are in general agreement on the effects of a finite volume fraction of coarsening phase on the coarsening behavior of two-phase systems. New work on transient Ostwald ripening is presented which illustrates the broad range of behavior which is possible in this regime. The conditions responsible for the presence of the asymptotic state first discovered by LS, as well as the manner in which this state is approached, are also discussed. The role of elastic fields during Ostwald ripening in solid-solid mixtures is reviewed, and it is shown that these fields can play a dominant role in determining the coarsening behavior of a solid-solid system.