We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction strength behaves as 1/T . We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an ...

We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of “almost Gibbsian measures” (almost sure continuity of conditional probabilities). For quasilocal measures, we obtain a full variational principle. For the joint measures of the random field Ising model, we show ...

From measurements of the surface tension, density, viscosity and light scattering of aqueous solutions of methanol, ethanol and propanol at 293 K, their activity in the surface monolayer, surface excess concentration, and apparent and partial molar volume were determined. The surface excess concentration of alcohols at the water-air interface was determined from the Gibbs equation by using both...

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions , mixing and ergodicity in Gibbs Γ-space. What are the corresponding hypothesis for nonextensive statistical mechanics? A scenario for ...

In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs’ distributions by introducing low dimensional perturbations and solving the corresponding MAP assignments. Our approach also leads to new ways to derive lower bounds on partition functions. We demonst...

Using Sm-doped Ceria electrolytes (SDC) in SOFCs (solid oxide fuel cell), the open circuit voltage (OCV) becomes lower than the Nernst voltage (Vth), which is obtained using Yttria-stabilized Zirconia (YSZ) electrolytes. Classically, OCV is calculated with Wagner’s equation. However, experimental verification of leakage currents using SDC electrolytes is necessary, both qualitatively and quanti...

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross...

The thermodynamic quantities of Lennard-Jones gases, evaluated till the fourth virial coefficient, are investigated for an isobaric process. A partition function in the T -P grand canonical ensemble Y (T,P,N) may be defined by the Laplace transform of the partition function Z(T,V,N) in the canonical ensemble. The Gibbs free energy is related with Y (T,P,N) by the Legendre transformation G(T,P,N...

We start with an explanation of Simulated Annealing. In order to do this, we quote the paper “Convergence of Gibbs Measures Associated with Simulated Annealing” [CHK], by professors Dennis Cox of the Rice University Statistics department, Robert Hardt of the Rice University Mathematics department, and Petr Klouček of the University of Houston Texas Learning and Computation Center, which states ...

Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper, we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The G...