We examine several variational methods for determining bounds on the free energy of model crystalline phases, as applied to hard spheres in one and three dimensions. Celland harmonic-based reference systems are considered. Methods that provide the tightest bounds on the free energy are similar in form to free-energy perturbation, and are prone to inaccuracy from inadequate sampling. Gibbs–Bogol...

Gibbs paradox statement of entropy of mixing has been regarded as the theoretical foundation of statistical mechanics, quantum theory and biophysics. A large number of relevant chemical and physical observations show that the Gibbs paradox statement is false. We also disprove the Gibbs paradox statement through consideration of symmetry, similarity, entropy additivity and the defined property o...

Modelling of spatially homogeneous and piecewise-homogeneous image textures by novel Markov and non-Markov Gibbs random fields with multiple pairwise pixel interactions is briefly overviewed. These models allow for learning both the structure and strengths (Gibbs potentials) of the interactions from a given training sample. The learning is based on first analytic and then stochastic approximati...

Thermodynamic expressions are derived for the system relative Gibbs free energy, and the relative Gibbs free energy per bubble, for all possible equilibrium bubble states that can form in a soft slightly rigid material, initially supersaturated with a dissolved inert gas (N(2)). While the thermodynamic manipulations are exact, the final expressions are approximate, due to an approximation made ...

Prediction of stable mineral equilibria in the Earth's lithosphere is critical to unravel tectonomagmatic history exposed geological sections. While recent advances geodynamic modeling allow us explore dynamics magmatic transfer solid mediums, there date no available thermodynamic package that can easily be linked and efficiently accounted for computation phase equilibrium systems. Moreover, no...