The Helmholtz free energy of oscillators in thermal equilibrium with electromagnetic radiation is obtained from the Pauli-Hellmann-Feynman theorem and applied to some aspects Lamb shifts van der Waals interactions.

Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms have been shown to correspond to extrema of the Bethe and Kikuchi free energy, both of which are approximations of the exact Helmholtz free energy. However, belief propagation does not always converge, which motivates approache...

In this paper, we develop further the theory of thermostated systems along the lines of our earlier paper ([1] Fox). Two results are highlighted: 1) in the Markov limit of the contracted description, a least dissipation of Helmholtz free energy principle is established; and 2) a detailed account of the appropriateness of this principle for nanobiology, including the evolution of life, is presen...

In this paper, we extend the quasicontinuum approach for a multiscale analysis of silicon nanostructures at finite temperature. The quasicontinuum method uses the classical continuum mechanics framework, but the constitutive response of the system is determined by employing an atomistic description. For finite-temperature solid systems under isothermal conditions, the constitutive response is d...

We study a model initially proposed to describe a mixture of (CO) 1−x (N 2) x adsorbed on exfoliated graphite. The approach used here is that of mean field theory. The Mean Field equations and the Helmholtz Free Energy are found. Phase diagrams are calculated too, and it is possible to find an analytic expression for the second order phase transition line.

The constant pressure-temperature (P− T ) flash plays an important role in the modelling of fluid-phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P− T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy e...

This paper addresses the development of a free energy model for magnetostrictive transducers operating in hysteretic and nonlinear regimes. Such models are required both for material and system characterization and for model-based control design. The model is constructed in two steps. In the first, Helmholtz and Gibbs free energy relations are constructed for homogeneous materials with constant...