In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by the external force and alters the Gaussian structure of the system's fluctuations. By solving this extended equation, we demonstrate that the statistical properties of the fluctuations in these systems can be predicted from physical observables, such as the temperature and the hydrodynamic gradients.

We calculated the thermodynamic and thermoelastic properties of periclase and ferropericlase, the latter having a stoichiometric composition of (Fe 0.03 Mg 0.97 )O, at pressures and temperatures which are typical of the Earth's lower mantle. The static lattice energies and vibrational frequencies were derived through ab-initio calculations carried out at the hybrid HF/DFT level. The thermodynamic properties were calculated by following a standard statistical-thermodynamics approach, within the limit of the quasi-harmonic approximation. A third order Birch-Murnaghan equation of state fit to the static E(V) data of periclase yielded K 0 = 163.8 GPa, K' = 4.3 and V 0 = 75.09 Å 3 . The fit at 300K and 0.1 MPa on the P(V) data yielded K 0 = 160.1 GPa, K' = 4.2 and V 0 = 75.99 Å 3 . Such results successfully reproduced the best available experimental and previous computational data. The presence of iron with low spin configuration in the structure had the effects (i) to reduce the cell volume, both at the static (74.19 Å 3 ) and at the ambient conditions (75.14 Å 3 ); (ii) to increase the bulk modulus (respectively 172.2 GPa at the static limit, and 167.4 GPa at 298 K and 0.1 MPa) and (iii) to decrease the thermal expansion (2.79*10 -5 K -1 for periclase and 2.60*10 -5 K -1 for ferropericlase at 300 K). Since the discussed parameters were also calculated at high pressure and temperature conditions simultaneously, the reliability of the quasi-harmonic approximation was tested by evaluating the shape of the potential energy curve, at conditions which simulate those of the Earth's lower mantle. Such test confirmed the applicability of this approximation over all the P/T range considered.

A new program package based on the Microsoft Windows operational systems is proposed for thermal investigations of crystals. The package consists of two programs, one of which provides a means for calculating the thermal expansion tensor for crystals of any symmetry and the second program is intended for drawing three-dimensional thermal expansion diagrams. The calculation and drawing procedures are described.

First-passage time statistics of water molecules carries information about their interaction with proteins. This information allows reconstruction of water’s space-dependent mobility near protein surfaces.

By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating variables, including hydrodynamic currents, in equilibrium as well as nonequilibrium steady states. From the solution of the obtained stochastic equations we derive an analytical expression for the time autocorrelation function of a general fluctuating quantity. This theoretical result is then tested in a study of a shear flow by molecular dynamics simulations. The proposed form of the time autocorrelation function yields an excellent fit to our computational data for both equilibrium and nonequilibrium steady states. Unlike the analogous result of the first-order Onsager-Machlup theory, our expression correctly describes the short-time correlations. Its utility is demonstrated in an application of the Green-Kubo formula for the transport coefficient. Curiously, the normalized time autocorrelation function for the shear flow, which only depends on the deterministic part of the fluctuation dynamics, appears independent of the external shear force in the linear nonequilibrium regime.