On the radial distribution function of a hard-sphere fluid

Structural and thermodynamic properties of hard-sphere fluids

This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions linking the equation of state of the single-component fluid to the one of the multicomponent mixtures are also discussed.

Interplay of reactive interference and crowding effects in the diffusion-influenced reaction kinetics

We investigate the interplay of reactive interference and crowding effects in the irreversible diffusion-influenced bimolecular reactions of the type A+B→P+B by using the Brownian dynamics simulation method. It is known that the presence of nonreactive crowding agents retards the reaction rate when the volume fraction of the crowding agents is large enough. On the other hand, a high concentration of B is known to increase the reaction rate more than expected from the mass action law, although the B's may also act as crowders. Therefore, it would be interesting to see which effect dominates when the number density of B as well as the number density of the crowders increases. We will present an approximate theory that provides a reasonable account for the Brownian dynamics simulation results.

Ex Machina Determination of Structural Correlation Functions

Determining the structural properties of condensed-phase systems is a fundamental problem in theoretical statistical mechanics. Here we present a machine learning method that is able to predict structural correlation functions with significantly improved accuracy in comparison with traditional approaches. The usefulness of this ex machina (from the machine) approach is illustrated by predicting the radial distribution functions of two paradigmatic condensed-phase systems, a Lennard-Jones fluid and a hard-sphere fluid, and then comparing those results to the results obtained using both integral equation methods and empirically motivated analytical functions. We find that application of the developed ex machina method typically decreases the predictive error by more than an order of magnitude in comparison with traditional theoretical methods.

Thermostatistics of small nonlinear systems: Gaussian thermal bath

We discuss the statistical properties of small mechanothermodynamic systems (one- and two-particle cases) subject to nonlinear coupling and in contact with standard Gaussian reservoirs. We use a method that applies averages in the Laplace-Fourier space, which relates to a generalization of the final-value theorem. The key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator, traditionally required in alternative methods like path integral calculations, which is hardly obtainable in the majority of the cases. For one-particle equilibrium systems we are able to compute the instantaneous (equilibrium) probability density functions of injected and dissipated power as well as the respective large deviation functions. Our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long-term statistics, which preserve the exact same values as computed for linear cases. Actually, we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium, since it affects the average total energy of the system. For the two-particle system we consider each element in contact with a heat reservoir, at different temperatures, and focus on the problem of heat flux between them. Contrarily to the one-particle case, in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system. An important consequence of that it is the temperature dependence of the conductance, which is unobserved in linear(harmonic) models. Our results are complemented by fluctuation relations for the injected power (equilibrium case) and heat flux (nonequilibrium case).