A thermodynamic property model explicit in the Helmholtz energy is presented for the R-134a/245fa mixtures. A multi-fluid approximation based on pure-fluid Helmholtz energy equations of state forms the basis of the property model. The Helmholtz energy of the mixture is expressed as the sum of the ideal gas contribution, the compressibility contribution (real fluid contribution), and the contrib...

We present a formulation of mean-field approximation for layered feed-forward stochastic networks. In this formulation, one can obtain not only estimates of averages for state variables of the networks but also those of intra-layer correlations, the latter of which cannot be obtained by the conventional mean-field approximation. Moreover, this formulation provides a framework to treat “conditio...

Starting from the Helmholtz free energy we calculate analytically first-and second-order derivatives, as internal energy and specific heats, for the ideal system and the exchange and correlation interactions covering a broad range of degeneracy and relativity. The complex physics of Coulomb interactions is expressed by Padé Approximants, which reflect the actual state of our knowledge with high...

The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of General Relativity. When the variation of the energy is written in a covariant form it splits into two (covariant) contributions: one of them is the Komar energy, while the other is the so–called covariant ADM correction term. When specific boundary conditions are analyzed one sees...

The Jarzynski identity [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and the Crooks equation [G. E. Crooks, J. Stat. Phys. 90, 1481 (1998)] relate thermodynamic free energy differences to the work done on a system during a collection of nonequilibrium transformations. In the present Rapid Communication we provide generalized versions of these nonequilibrium work theorems, which hold for diss...

We study the effective potential of three-dimensional O(N) models. In statistical physics the effective potential represents the free-energy density as a function of the order parameter (Helmholtz free energy), and, therefore, it is related to the equation of state. In particular, we consider its small-field expansion in the symmetric (high-temperature) phase, whose coefficients are related to ...

We consider a continuum model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the governing equations. In the model, the Helmholtz free energy and Rayleigh dissipation are used, within a Lagrangian framework, to obtain the equations of motion. The free energy consists of both elastic and liquid crystalline contributions, each...

Equilibrium properties of dilute binary fluid mixtures are studied in two-phase states on the basis of a Helmholtz free energy including the gradient free energy. The solute partitioning between gas and liquid (Henry's law) and the surface tension change Delta gamma are discussed. A derivation of the Gibbs law Delta gamma = -T Gamma is given with Gamma being the surface adsorption. Calculated q...