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Part I. Measures the dynamic surface force using the van der Waals collisions. Effect of cantilever deflection on speed and magnitude of surface force; Details on the collision-induced elastic vibrations in the solids; Factors attributing the surface separation at high accelerations.

A mutant version of the N-terminal domain of Escherichia coli DnaB helicase was used as a model system to assess the stabilization against unfolding gained by covalent cyclization. Cyclization was achieved in vivo by formation of an amide bond between the N and C termini with the help of a split mini-intein. Linear and circular proteins were constructed to be identical in amino acid sequence. Mutagenesis of Phe102 to Glu rendered the protein monomeric even at high concentration. A difference in free energy of unfolding, ΔΔG, between circular and linear protein of 2.3(±0.5)kcalmol−1 was measured at 10°C by circular dichroism. A theoretical estimate of the difference in conformational entropy of linear and circular random chains in a three-dimensional cubic lattice model predicted ΔΔG=2.3kcalmol−1, suggesting that stabilization by protein cyclization is driven by the reduced conformational entropy of the unfolded state. Amide-proton exchange rates measured by NMR spectroscopy and mass spectrometry showed a uniform, approximately tenfold decrease of the exchange rates of the most slowly exchanging amide protons, demonstrating that cyclization globally decreases the unfolding rate of the protein. The amide proton exchange was found to follow EX1 kinetics at near-neutral pH, in agreement with an unusually slow refolding rate of less than 4min−1 measured by stopped-flow circular dichroism. The linear and circular proteins differed more in their unfolding than in their folding rates. Global unfolding of the N-terminal domain of E.coli DnaB is thus promoted strongly by spatial separation of the N and C termini, whereas their proximity is much less important for folding. [Copyright &y& Elsevier]

A general theory for the stability and coexistence of nonequilibrium phases is formulated. An integral formulation of the second entropy is given, the functional maximization of which yields nonlinear hydrodynamics. Rayleigh-Bénard convection is analyzed, and analytic approximations are obtained for the second entropy for conduction and for convection. Despite the simplicity of the model, coexistence is predicted for a Rayleigh number within 5% of the known value.

The general form for the probability density and for the transition probability of a nonequilibrium system is given. Maximization of the latter gives a generalized fluctuation-dissipation theorem by providing a molecular basis for Langevin's friction force that avoids continuum hydrodynamics. The result shows that the friction coefficient must be proportional to the variance of the stochastic equations of motion. Setting the variance to zero but keeping the friction coefficient nonzero reduces the theory to a Hoover thermostat without explicit constraint, although such a limit violates the physical requirement of proportionality between the dissipation and the fluctuation. A stochastic molecular dynamics algorithm is developed for both equilibrium and nonequilibrium systems, which is tested for steady heat flow and for a time-varying, driven Brownian particle.

The atomic force microscope was employed to investigate the time effect on normal interactions between a hydrophilic silica particle and an air bubble deposited onto a hydrophobic Teflon surface in pure water and 10 mM methyl isobutyl carbinol solutions. The force versus separation distance curves taken at different times after bubble generation were qualitatively compared. It has been found that the penetration distance, jump-in force, contact angle, rupture distance, force required for the film to rupture, interfacial spring constant, and bubble shape were time-dependent. The results were explained by the change of the air-water interface shape with time due to water droplet growth on the Teflon surface inside the air bubbles.

A Brownian particle subject to a time- and space-varying force is studied with the second entropy theory for nonequilibrium statistical mechanics. A fluctuation expression is obtained for the second entropy of the path, and this is maximized to obtain the most likely path of the particle. Two approaches are used, one based on the velocity correlation function and one based on the position correlation function. The approaches are a perturbation about the free particle result and are exact for weak external forces. They provide a particularly simple way of including memory effects in time-varying driven diffusion. The theories are tested against computer simulation data for a Brownian particle trapped in an oscillating parabolic well. They accurately predict the phase lag and amplitude as a function of drive frequency, and they account quantitatively for the memory effects that are important at high frequencies and that are missing in the simplest Langevin equation.

The authors study the transport of mass and heat in simulations of a Lennard-Jones fluid and demonstrate the calculation of transport coefficients, and of both the first and second entropies. These entropies are calculated from time correlation functions, as are the transport coefficients. They discuss the role of the second entropy in providing a physical explanation for the link between dynamic fluctuations and response. They illustrate the physical significance of the various contributions to the second entropy and how they simplify in the case of relaxation by steady-state flow. Certain approximations proposed for the calculation of the first entropy, common in the literature, are shown to break down under certain circumstances, and they give an improved method of calculation. They pay particular attention to the coupling between variables of opposite time parity in the transport matrix, and show that in general this cannot be neglected.

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. Its asymmetric part contributes to the flux and to the production of second entropy. The nonlinear transport matrix is not simply expressible as a Green-Kubo fluctuation equilibrium time correlation function. However, here the first nonlinear correction to the transport coefficient is given explicitly as a type of the Green-Kubo equilibrium time correlation function. The theory is illustrated by application to chemical kinetics.

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.

The phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent mechanical work, and for nonequilibrium quantum statistical mechanics.

Two microscopic transition theorems are given for the probability of nonequilibrium work performed on a subsystem of a thermal reservoir along the trajectory in phase space of the subsystem. The resultant transition probability is applied to the case of heat flow down an applied temperature gradient. A combined molecular dynamics and Monte Carlo algorithm is given for such a nonequilibrium steady state. Results obtained for the thermal conductivity are in good agreement with previous Green-Kubo and nonequilibrium molecular dynamics results.

A statistical mechanical theory for heat flow is developed based upon the second entropy for dynamical transitions between energy moment macrostates. The thermal conductivity, as obtained from a Green-Kubo integral of a time correlation function, is derived as an approximation from these more fundamental theories, and its short-time dependence is explored. A new expression for the thermal conductivity is derived and shown to converge to its asymptotic value faster than the traditional Green-Kubo expression. An ansatz for the steady-state probability distribution for heat flow down an imposed thermal gradient is tested with simulations of a Lennard-Jones fluid. It is found to be accurate in the high-density regime at not too short times, but not more generally. The probability distribution is implemented in Monte Carlo simulations, and a method for extracting the thermal conductivity is given.

A method of calculating rates of homogeneous vapor-liquid nucleation based on Langevin dynamics of a few relevant degrees of freedom on a free-energy surface is proposed. The surface is obtained here from simulation and from a semi empirical expression. The mass and friction coefficients are derived from atomistic umbrella-sampling molecular-dynamics simulations. The calculated nucleation rate agrees with atomistic simulations for one particular state point of the Lennard-Jones fluid. The present method is about four orders of magnitude more computationally efficient than the direct atomistic simulation of the transmission coefficient.

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method. The Green-Kubo formulas for the transport coefficients emerge from the analysis, as do Langevin dynamics.

The constrained entropy and probability distribution are given for the structure that develops in response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory is linear but is applicable to gradients with arbitrary spatial variation. The phase space probability distribution is also given, and it is surprisingly simple with a straightforward physical interpretation. With it, all of the known methods of equilibrium statistical mechanics for inhomogeneous systems may now be applied to determining the structure of nonequilibrium steady state systems. The theory is illustrated by performing Monte Carlo simulations on a Lennard-Jones fluid with externally imposed temperature and chemical potential gradients. The induced energy and density moments are obtained, as well as the moment susceptibilities that give the rate of change of these with imposed gradient and which also give the fluctuations in the moments. It is shown that these moment susceptibilities can be written in terms of bulk susceptibilities and also that the Soret coefficient can be expressed in terms of them.

A systematic study into the effect of solid roughness on the slip boundary condition during shear flow is presented. Atomic roughness is modeled by varying the size and spacing between solid atoms at constant packing fraction while the interaction parameters and the thermodynamic state of the fluid are kept constant. It is shown that the fluid structure as manifest in the amplitude of the density oscillations increases with increasing smoothness of the surfaces. The fluid-solid slip length is shown to exhibit nonmonotonic behavior as the solid structure is varied from smooth to rough. Slip occurs for both smooth and rough surfaces, and stick occurs only for surfaces commensurate with the fluid.

A novel "ghost interface" expression for the surface tension of a planar liquid-vapor interface is derived in detail from consideration of the free energy of the system, and a methodology for utilization of this new technique is given. An augmented Monte Carlo computer simulation procedure is developed specifically for the ghost interface, including derivation of long-range corrections resulting from potential truncation and a modified Gibbs ensemble technique for the simulation of adjacent coexisting phases. Results generated from the ghost interface theory for the surface tension are presented and found to be in good quantitative agreement with those resulting from the Kirkwood-Buff equation. Applications of this new approach to curved and to supersaturated systems are also discussed.

The evidence for nanobubbles as the origin of the long-ranged attractions measured between hydrophobic surfaces immersed in water is reviewed by focusing upon several unique features of the force curves. Also covered is the morphology of nanobubbles as revealed by direct imaging with tapping mode atomic force microscopy. A discussion of the origin, thermodynamic stability and practical implications of nanobubbles is given.