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We present high-resolution measurements of the pair interactions between dielectric spheres dispersed in a fluid medium with a low dielectric constant. Despite the absence of charge control agents or added organic salts, these measurements reveal strong and long-ranged repulsions consistent with substantial charges on the particles whose interactions are screened by trace concentrations of mobile ions in solution. The dependence of the estimated charge on the particles' radii is consistent with charge renormalization theory and, thus, offers insights into the charging mechanism in this interesting class of model systems. The measurement technique, based on optical-tweezer manipulation and artifact-free particle tracking, makes use of optimal statistical methods to reduce measurement errors to the femtonewton frontier while covering an extremely wide range of interaction energies.

The color-diffusion algorithm is applied to ab initio molecular dynamics simulation of hexagonal LiBH(4) to determine the lithium diffusion coefficient and diffusion mechanisms. Even in the best solid lithium ion conductors, the time scale of ion diffusion is too long to be readily accessible by ab initio molecular dynamics at a reasonable computational cost. In our nonequilibrium method, rare events are accelerated by the application of an artificial external field acting on the mobile species; the system response to this perturbation is accurately described in the framework of linear response theory and is directly related to the diffusion coefficient, thus resulting in a controllable approximation. The calculated lithium ionic conductivity of LiBH(4) closely matches published measurements, and the diffusion mechanism can be elucidated directly from the generated trajectory.

In the past decade there has been considerable interest in nonequilibrium free energy theorems. These theorems show how the difference between the free energies of two equilibrium states of a system are related to distributions of work along nonequilibrium pathways. Here we significantly extend these theorems by relating the possibly inaccessible equilibrium average of any phase variable to the distribution of work along nonequilibrium paths. The result is elegant and analogous to the static umbrella sampling used with Monte Carlo simulations. The umbrella weight, which is related to the nonequilibrium work, is easy to obtain and efficient to compute. Furthermore, its average may be obtained from the existing nonequilibrium free energy theorem.

The mathematics of time-dependent nonlinear response theory frequently leads to results which although formally exact, are not amenable to experimental application or even to use in computer simulations. Here we give a rigorous derivation of a tractable expression for the thermostatted nonlinear response of classical many body systems to time-dependent dissipative fields. The theory also allows for the concurrent parametric transformation of the system Hamiltonian. Our analysis shows once again the intimate relationship between nonequilibrium free-energy relations such as the Jarzynski equality and nonlinear response theory. We make a few remarks concerning the maximum entropy production approximation.

The Jarzynski equality and the Crooks fluctuation theorem enable the calculation of the change in a system's free energy from nonequilibrium path integrals. These relations consider processes where the system is driven out of equilibrium by a mechanical external agent while remaining in contact with a thermal reservoir at a fixed temperature. We generalize these relations to describe processes driven by any type of external agent, be it thermal or mechanical. Attention is given to the case of a system, initially in equilibrium, that is driven through a temperature change by a heat reservoir. The results are cast in a form applicable to experiments.

Molecular dynamics simulations are performed on a realistic glass forming model system. The linear and nonlinear response domains are explored numerically for the case where one of the particles interacts with a constant external force. As the temperature is lowered towards the glass transition, we find that the range of fields over which the response is linear shrinks towards zero. We show that the time required for convergence of the steady state fluctuation theorem and the valid application of the central limit theorem becomes very large as the glass transition is approached. This in turn implies that the domain over which a linear response can be observed becomes progressively smaller.

The fluctuation relation of the Gallavotti-Cohen fluctuation theorem (GCFT) concerns fluctuations in the phase-space compression rate of dissipative, reversible dynamical systems. It has been proven for Anosov systems, but it is expected to apply more generally. This raises the question of which non-Anosov systems satisfy the fluctuation relation. We analyze time-dependent fluctuations in the phase space compression rate of a class of N-particle systems that are at equilibrium or in near equilibrium steady states. This class does not include Anosov systems or isoenergetic systems; however, it includes most steady-state systems considered in molecular-dynamics simulations of realistic systems. We argue that the fluctuations of the phase-space compression rate of these systems at or near equilibrium do not satisfy the fluctuation relation of the GCFT, although the discrepancies become somewhat smaller as the systems move further from equilibrium. In contrast, similar fluctuation relations for an appropriately defined dissipation function appear to hold both near and far from equilibrium.

The fluctuation theorem (FT) quantifies the probability of second law violations in small systems over short time scales. While this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state, there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state. The asymptotic application of the FT to such nonequilibrium steady states has been referred to in the literature as the steady-state fluctuation theorem (or SSFT). In this paper, we demonstrate experimentally the application of the FT to nonequilibrium steady states, using a colloidal particle localized in a translating optical trap. Furthermore, we show, for this colloidal system, that the FT holds under nonequilibrium steady states for all time, and not just in the long time limit, as in the SSFT.

The fluctuation theorems show how macroscopic irreversibility arises from time reversible microscopic dynamics. They have been confirmed in computer simulations and in laboratory experiments. The standard proofs of the transient fluctuation theorems involve the use of time reversible deterministic thermostats to control the temperature of the system of interest. These mathematical thermostats do not occur in Nature. However, since in a gedanken experiment the thermostatting regions can be removed arbitrarily far from the system of interest, it has been argued that the precise details of the thermostat cannot be important and that the resulting fluctuation theorems apply to natural systems. In this paper we give a detailed analysis showing how the fluctuation theorem is independent of the precise mathematical details of the thermostatting mechanism for an infinite class of fictitious time reversible deterministic thermostats. Our analysis reinforces the implications of the gedanken experiment and implies that thermostats used in the derivations of fluctuation theorems are a convenient but ultimately irrelevant device.

The puzzle of how time-reversible microscopic equations of mechanics lead to the time-irreversible macroscopic equations of thermodynamics has been a paradox since the days of Boltzmann. Boltzmann simply sidestepped this enigma by stating "as soon as one looks at bodies of such small dimension that they contain only very few molecules, the validity of this theorem [the second law of thermodynamics and its description of irreversibility] must cease." Today we can state that the transient fluctuation theorem (TFT) of Evans and Searles is a generalized, second-law-like theorem that bridges the microscopic and macroscopic domains and links the time-reversible and irreversible descriptions. We apply this theorem to a colloidal particle in an optical trap. For the first time, we demonstrate the TFT in an experiment and show quantitative agreement with Langevin dynamics.

The fluctuation theorem (FT) describes how a system's thermodynamic irreversibility develops in time from a completely thermodynamically reversible system at short observation times, to a thermodynamically irreversible one at infinitely long times. In this paper, we present a general definition of the dissipation function Omega(t), the quantitative argument in the fluctuation theorem (FT), that is a measure of a system's irreversibility. Originally cast for deterministic systems, we demonstrate, through the example of two recent experiments, that the dissipation function can be defined for stochastic systems. While the ensemble average of Omega(t) is positive definite irrespective of the system for which it is constructed, different expressions for Omega(t) can arise in stochastic and deterministic systems. Moreover, within the stochastic framework, Omega(t) is not unique. Nevertheless, each of these expressions for Omega(t) satisfies the FT.

In 1984, Erpenbeck observed a shear-induced alignment of particles into strings in nonequilibrium molecular dynamics simulations of hard spheres. Since then, it has remained unclear if this effect was genuine or if it arose from the use of a thermostat which assumed an incorrect form for the velocity profile. All studies performed up to now have focused on improving the accuracy with which the velocity profile is determined. We propose here a radically different approach: we apply a recently developed configurational expression for the temperature. This expression does not require any knowledge of the streaming velocity profile. Using a configurational thermostat, we show that the string phase is an artifact and we observe a shear-thickening regime, as seen in experiments on concentrated "hard-sphere"-like colloidal dispersions.

The fluctuation theorem (FT) is a generalization of the second law of thermodynamics that applies to small systems observed for short times. For thermostated systems it gives the probability ratio that entropy will be consumed rather than produced. In the present paper, we propose a version of the FT that applies to thermostated dissipative systems which respond to time-dependent dissipative fields. In testing the time-dependent fluctuation theorem we provide convincing evidence that sets of trajectories with conjugate values for the time-integrated entropy production, (+/-A+/-deltaA), are indeed (for time-reversible dynamical systems such as those studied here), time-reversal images of one another. This observation verifies the deep connection between time-reversal symmetry, the fluctuation theorem, and the second law of thermodynamics.

We experimentally demonstrate the fluctuation theorem, which predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales, by following the trajectory of a colloidal particle captured in an optical trap that is translated relative to surrounding water molecules. From each particle trajectory, we calculate the entropy production/consumption over the duration of the trajectory and determine the fraction of second law-defying trajectories. Our results show entropy consumption can occur over colloidal length and time scales.

A nonequilibrium molecular dynamics model of heat flow in one-dimensional lattices is shown to have multiple steady states for any fixed heat field strength f(e) ranging from zero to a certain positive value. We demonstrate that, depending on the initial conditions, there are at least two possibilities for the system's evolution: (i) formation of a stable traveling wave (soliton), and (ii) chaotic motion throughout the entire simulation. The percentage of the soliton-generating trajectories is zero for small field strength f(e), but increases sharply to unity over a critical region of the parameter f(e).

The shear viscosity can be calculated from the standard deviation of an equilibrium ensemble of time averages of the shear stress computed along finite duration phase space trajectory segments. The mean square of the segment averages of the shear stress is proportional to the shear viscosity and inversely proportional to the duration of the trajectory segments and the number of particles. We test the fluctuation relation for the shear viscosity and show that it provides a simple but viable means of computing the zero strain rate shear viscosity. We decompose the shear viscosity computed using this fluctuation method, into its "kinetic" and "configurational" components. We also calculate the relevant relaxation times. We compare the computed results with standard nonequilibrium molecular dynamics simulations. Finally we compute the bulk viscosity using an analogous fluctuation method.

For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.