Connecting density fluctuations and Kirkwood-Buff integrals for finite-size systems

Mauricio Sevilla; Robinson Cortes-Huerto

doi:10.1063/5.0076744

Home/Archive/arXiv

arXiv · 2110.14536

Connecting density fluctuations and Kirkwood-Buff integrals for finite-size systems

Mauricio Sevilla·Robinson Cortes-Huerto

View original source ↗Read source document ↗Export metadata ↓

Abstract

Kirkwood-Buff integrals (KBI) connect the microscopic structure and thermodynamic properties of liquid solutions. KBI are defined in the grand canonical ensemble and evaluated assuming the thermodynamic limit (TL). In order to reconcile analytical and numerical approaches, finite-size KBI have been proposed in the literature, resulting in two strategies to obtain their TL values from computer simulations. (i) The spatial block-analysis method in which the simulation box is divided into subdomains of volume $V$ to compute fluctuations of the number of particles. (ii) A direct integration method where a corrected radial distribution function and a kernel that accounts for the geometry of the integration subvolumes are combined to obtain KBI as a function of $V$. In this work, we propose a method that connects both strategies into a single framework. We start from the definition of finite-size KBI, including the integration subdomain and an asymptotic correction to the radial distribution function, and solve them in Fourier space where periodic boundary conditions are trivially introduced. The limit $q\to 0$, equivalent to the value of the KBI in the TL, is obtained via the spatial block-analysis method. When compared to the latter, our approach gives nearly identical results for all values of $V$. Moreover, all finite-size effect contributions (ensemble, finite-integration domains and periodic boundary conditions) are easily identifiable in the calculation. This feature allows us to analyse finite-size effects independently and extrapolate the results of a single simulation to different box sizes. To validate our approach, we investigate prototypical systems, including SPC/E water and aqueous urea mixtures.

Explore related subjects

cond-mat.stat-mech cond-mat.soft

Keep this discovery

BibTeX RIS

Mauricio Sevilla, Robinson Cortes-Huerto. 2021-10-27. Connecting density fluctuations and Kirkwood-Buff integrals for finite-size systems. https://doi.org/10.1063/5.0076744

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗

arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗

arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗