Free energy from molecular dynamics with multiple constraints

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to constrain the reaction coordinate to a constant value, but the metric tensor effect of the constraint on the sampled phase space distribution complicates this relation. The appropriately corrected expression for the potential of mean constraint force method (PMCF) for systems in which only the reaction coordinate is constrained was published recently. Here we will consider the general case of a system with multiple constraints. This situation arises when both the reaction coordinate and the ‘hard’ coordinates are constrained, and also in systems with several reaction coordinates. The obvious advantage of this method over the established thermodynamic integration and free energy perturbation methods is that it avoids the cumbersome introduction of a full set of generalized coordinates complementing the constrained coordinates. Simulations of n-butane and n-pentane in vacuum illustrate the method.     

Free energy and correlation lengths of quantum chains related to restricted solid-on-solid lattice models

An approach is presented for calculating the free energy as well as the correlation lengths of integrable quantum chains at arbitrary finite temperatures. The method is applied to critical Hamiltonians related to restricted solid-on-olid models comprising the hierarchy by Andrews, Baxter and Forrester, and generalizations hereof by the fusion procedure. The derived non-linear integral equations can be studied analytically in the low-temperature and high-temperature limits. The central charges and all primary conformal weights are obtained for the generalized minimal unitary series of conformal field theory and the Z_N parafermion theories. Thus an extension of the thermodynamic Bethe Ansatz is realized which recently has been speculated on in the literature.     

Free energy of electrolyte solutions

The energy of formation of ionic hydrate complexes in infinitely dilute solutions was calculated using the molecular mechanics method. It was found that the OPLS force field is most preferable for calculating the energy of ionic hydration. A correlation relationship between the calculated and experimental energies of ion hydration was derived.     

Free energy of gravitating fermions

We calculate rigorously, in a suitable thermodynamic limit, the free energy of a system of nonrelativistic fermions which interact with attractiver ^–1-potentials. It is shown that the effective field approximation becomes exact in this limit and results in the temperature-dependent Thomas-Fermi equations.On leave of absence from the University of Heidelberg, Germany.On leave of absence from the University of Vienna, Austria.     

Potential energy surface of alanine polypeptide chains

The multidimensional potential energy surfaces of the peptide chains consisting of three and six alanine (Ala) residues have been studied with respect to the degrees of freedom related to the twist of these molecules relative to the peptide backbone (these degrees of freedom are responsible for the folding of such peptide molecules and proteins). The potential energy surfaces have been calculated ab initio within the framework of the density functional theory taking into account all electrons in the system. The probabilities of transitions between various stable conformations of polypeptide molecules are evaluated. The results are compared to the data obtained by molecular dynamics simulations and to the available experimental data. The influence of the secondary structure of the polypeptide chain on its conformational properties with respect to rotations has been studied. It is shown that, in a chain of six amino acid (Ala) residues, the secondary structure type (helix or sheet conformation) influences the stable isomer states of the polypeptide.     

Free energy of a spin glass

We give the theory of a model spin glass of the Sherrington-Kirkpatrick type. Determining that the free energy is given by the potential function of a two-dimensional electrostatic medium, we find exact expressions for this quantity in terms of a multipole expansion of the charge distribution. We also obtain the internal energy, entropy, and specific heat in the form of explicit integrals over the multipole distributions. Pending the outcome of a quantitative investigation into the structure of these functions, here we discuss their properties in a qualitative way.     

Free energy cascade in gyrokinetic turbulence

In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.     

Free energy and the relative entropy

Under the assumption of an identity determining the free energy of a state of a statistical mechanical system relative to a given equilibrium state by means of the relative entropy, it is shown: first, that there is in any physically definable convex set of states a unique state of minimum free energy measured relative to a given equilibrium state; second, that if a state has finite free energy relative to an equilibrium state, then the set of its time translates is a weakly relatively compact set; and third, that a unique perturbed equilibrium state exists following a change in Hamiltonian that is bounded below.     

Free energy of nonideal two-component thermal plasma

The free energy of nonideal two-component thermal plasma is calculated using the Poisson-Boltzmann equation. The possibility of the existence of a metastable state is shown for a component of heavy multicharged particles with particle charge values bounded from below and plasma temperature values bounded from above. The component of oppositely-charged light singly-charged particles and plasma generally do not feature the metastable state.     

Free energy of a Lovelock holographic superconductor

We study thermodynamics of black hole solutions in Lanczos–Lovelock anti-de Sitter gravity in \(d+1\) dimensions coupled to nonlinear electrodynamics and a Stückelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in \(d\) dimensions. A larger number of coupling constants in the gravitational side is necessary to widen the domain of validity of physical quantities in dual quantum field theory (QFT). We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and we obtain the exact formula for the free energy of the superconductor in the holographic QFT. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.     

Fluorescence and host-guest energy transfer in polymeric chains

Intrachain singlet electronic excitation energy transfer from host polyvinylcarbazole (PVCa) to guest vinylbenzocarbazole (VBCa) units has been studied through measurements of the quenching effect on PVCa fluorescence and observation of the sensitized guest VBCa emission in solutions at 293 and 77K for different intramolecular concentrations of guest VBCa units. A method of taking into account intrinsic traps of singlet excitons (excimer forming sites, EFS), ordinarily present in an impurity free polymer macromolecule, has been elaborated. The comparison of the experimental data with theory shows that the one-dimensional singlet excitation energy transfer in a polymeric chain involves motion of incoherent excitons randomly hopping to a nearest neighbor along the line under conditions when capturing occurs upon the first visit of a trap and trapping centers of different origin become indistinguishable as regards their capturing capability.     

On multiple phase transitions for branching Markov chains

We consider branching Markov chains on a countable set. We give a necessary and sufficient condition in terms of the transition kernel of the underlying Markov chain to have two phase transitions. We compute the critical values. We apply this result to prove that asymmetric branching random walks onZ have two phase transitions.     

Free energy of segregation at alloy surfaces

The free energy of segregation at semi-infinite solid binary alloy surfaces is calculated using a quasi-chemical approach. The alloy is treated to be a non-regular solution. The concentration is assumed to be different only at the surface layer. The theory is applied to AgAu alloys. The concentration and the short-range-order parameters at the surface are calculated.