arXiv subjects

Luigi Delle Site

Publications and source records attributed to Luigi Delle Site.

At least 19 recordsLinked to original sources

arXiv2026

The two-sided Bogoliubov inequality in von Neumann algebras conceptualizes the free energy--quantum correlations link

The quantum-mechanical two-sided Bogoliubov inequality provides upper and lower bounds for the free energy required to separate a system of interacting particles into independent subsystems. The bounds can be calculated straightforwardly from the ensemble average of the interface energy, bypassing the direct evaluation of the free energy. In this work, we generalize the two-sided Bogoliubov inequality to arbitrary von Neumann algebras by employing the Araki-Uhlmann relative entropy and the framework of unbounded perturbation theory of KMS states. Furthermore, we obtain variational expressions for the relative free energy that extend existing bounded-perturbation principles to the unbounded setting. Crucially, these mathematical developments yield a physically well-founded thermodynamic criterion for the quantification of entanglement in infinite-dimensional systems.

math-ph↗

arXiv2026

Physico-mathematical model of open quantum systems with varying particle number

We derive the effective Hamiltonian $H - μN$ for open quantum systems with varying particle number from first principles. Our derivation relies on the general postulates of quantum statistical mechanics and on some specific assumptions regarding the size of the open system and the range of the interaction with the reservoir. Within this model, we also show that the effective Hamiltonian is unique up to a constant. In the course of our argument, we establish a rigorous version of the surface-to-volume ratio approximation, which is routinely used in an empirical form in statistical physics, and we show that the Hilbert space for systems with varying particle number must be isomorphic to Fock space. Together, these findings establish a solid physico-mathematical model for open quantum systems with varying particle number.

math-ph↗

arXiv2026

Open quantum systems beyond equilibrium: Lindblad equation and path integral molecular dynamics

The Lindblad equation determines the time evolution of the density operator of open quantum systems. While valid for any system size, its use is, in practice, restricted to prototype/surrogate models with the aim of tackling specific aspects of the overall quantum complexity of a multi-atomic system. Path integral molecular dynamics (PIMD) instead provides static and dynamical quantum statistical averages of physical observables for systems in equilibrium composed of up to thousands of atoms over timescales up to nanoseconds, under the condition that short-time quantum coherence is not relevant for the properties of interest. PIMD relies on the well-established technique of molecular dynamics (MD) with its associated classical trajectories. However, it cannot describe a direct time evolution of a system and its convergence to a stationary state in situations out of equilibrium. In this work, we analyze the link between the Lindblad equation and PIMD; specifically, we will discuss how PIMD can actually be used to calculate the time evolution of ensemble-averaged physical observables and their convergence to a stationary state for situations out of equilibrium, bypassing the need of explicitly solving the Lindblad equation. Yet, at the same time, the Lindblad equation and PIMD are linked to one another through a formal relation of equivalence, which provides an argument for the consistency of PIMD results, namely the positivity of the density operator at any time. A numerical study of a prototype system, which is of interest in chemical physics, will be used to showcase the method.

quant-ph↗

arXiv2025

A fast and rigorous numerical tool to measure length-scale artifacts in molecular simulations

The two-sided Bogoliubov inequality for classical and quantum many-body systems is a theorem that provides rigorous bounds on the free-energy cost of partitioning a given system into two or more independent subsystems. This theorem motivates the definition of a quality factor which directly quantifies the degree of statistical-mechanical consistency achieved by a given simulation box size. A major technical merit of the theorem is that, for systems with two-body interactions and a known radial distribution function, the quality factor can be computed by evaluating just two six-dimensional integrals. In this work, we present a numerical algorithm for computing the quality factor and demonstrate its consistency with respect to results in the literature obtained from simulations performed at different box sizes.

physics.comp-ph↗

arXiv2025

Open quantum systems and the grand canonical ensemble

The celebrated Lindblad equation governs the non-unitary time evolution of density operators used in the description of open quantum systems. It is usually derived from the von Neumann equation for a large system, at given physical conditions, when a small subsystem is explicitly singled out and the rest of the system acts as an environment whose degrees of freedom are traced out. In the specific case of a subsystem with variable particle number, the equilibrium density operator is given by the well-known grand canonical Gibbs state. Consequently, solving the Lindblad equation in this case should automatically yield, without any additional assumptions, the corresponding density operator in the limiting case of statistical equilibrium. Current studies of the Lindblad equation with varying particle number assume, however, the grand canonical Gibbs state a priori: the chemical potential is externally imposed rather than derived from first principles, and hence the corresponding density operator is not obtained as a natural solution of the equation. In this work, we investigate the compatibility of grand canonical statistical mechanics with the derivation of the Lindblad equation. We propose an alternative and complementary approach to the current literature that consists in using a generalized system Hamiltonian which includes a term $μN$. In a previous paper, this empirically well-known term has been formally derived from the von Neumann equation for the specific case of equilibrium. Including $μN$ in the system Hamiltonian leads to a modified Lindblad equation which yields the grand canonical state as a natural solution, meaning that all the quantities involved are obtained from the physics of the system without any external assumptions.

quant-ph↗

arXiv2025

Chemical potential and variable number of particles control the quantum state: Quantum oscillators as a showcase

Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit, we apply a model of a Hamiltonian for open quantum systems in equilibrium with a particle reservoir to ensembles of quantum oscillators. By treating (i) a dilute gas of vibrating particles and (ii) a chain of coupled oscillators as showcases, we demonstrate that the property of varying number of particles leads to a mandatory condition on the energy of the system. In particular, the chemical potential plays the role of a parameter of control that can externally manipulate the spectrum of a system and the corresponding accessible quantum states.

quant-ph↗

arXiv2024

Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems

A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we review complementary physico-mathematical approaches of varying number of particles inspired by rather different specific numerical goals. As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics.

math-ph↗

arXiv2024

Computationally feasible bounds for the free energy of nonequilibrium steady states, applied to simple models of heat conduction

In this paper we study computationally feasible bounds for relative free energies between two many-particle systems. Specifically, we consider systems out of equilibrium that do not necessarily satisfy a fluctuation-dissipation relation, but that nevertheless admit a nonequilibrium steady state that is reached asymptotically in the long-time limit. The bounds that we suggest are based on the well-known Bogoliubov inequality and variants of Gibbs' and Donsker-Varadhan variational principles. As a general paradigm, we consider systems of oscillators coupled to heat baths at different temperatures. For such systems, we define the free energy of the system relative to any given reference system (that may or may not be in thermal equilibrium) in terms of the Kullback-Leibler divergence between steady states. By employing a two-sided Bogoliubov inequality and a mean-variance approximation of the free energy (or cumulant generating function, we can efficiently estimate the free energy cost needed in passing from the reference system to the system out of equilibrium (characterised by a temperature gradient). A specific test case to validate our bounds are harmonic oscillator chains with ends that are coupled to Langevin thermostats at different temperatures; such a system is simple enough to allow for analytic calculations and general enough to be used as a prototype to estimate, e.g., heat fluxes or interface effects in a larger class of nonequilibrium particle systems.

cond-mat.stat-mech↗

arXiv2024

Scaling law for the size dependence of a finite-range quantum gas

In a recent work [Reible et al., Phys. Rev. Res. 5, 023156, 2023], it has been shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts, can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite range interactions that models a dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria.

cond-mat.stat-mech↗

arXiv2022

Simulation of a particle domain in a continuum/fluctuating hydrodynamics reservoir

In molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this work, we show a novel approach where the latest version of the adaptive resolution scheme (AdResS), with non-interacting tracers as particles reservoir, is combined with a fluctuating hydrodynamics (FHD) solver. The resulting algorithm, supported by a solid mathematical model, allows for a physically consistent exchange of matter and energy between the particle domain and its fluctuating continuum reservoir. Numerical tests are performed to show the validity of the algorithm. Differently from previous algorithms of the same kind, the current approach allows for simulations where, in addition to density fluctuations, also thermal fluctuations can be accounted for, thus large complex molecular systems, as for example hydrated biological membranes in a thermal field, can now be efficiently treated.

physics.comp-ph↗

arXiv2022

Two-sided Bogoliubov inequality to estimate finite size effects in quantum molecular simulations

We generalise the two-sided Bogoliubov inequality for classical particles from [L. Delle Site et al., J.Stat.Mech.Th.Exp. 083201 (2017)] to systems of quantum particles. As in the classical set-up, the inequality leads to upper and lower bounds for the free energy difference associated with the partitioning of a large system into smaller, independent subsystems. From a thermodynamic modelling point of view, the free energy difference determines the finite size correction needed to consistently treat a small system as a representation of a large system. Applications of the bounds to quantify finite size effects are ubiquitous in physics, chemistry, material science, or biology, to name just a few; in particular it is relevant for molecular dynamics simulations in which a small portion of a system is usually taken as representative of the idealized large system.

math-ph↗

arXiv2021

On the relation between pressure and coupling potential in adaptive resolution simulations of open systems in contact with a reservoir

In a previous paper [Gholami et al. Adv.Th.Sim.4, 2000303 (2021)], we have identified a precise relation between the chemical potential of a fully atomistic simulation and the simulation of an open system in the adaptive resolution method (AdResS). The starting point was the equivalence derived from the statistical partition functions between the grand potentials, $Ω$, of the open system and of the equivalent subregion in the fully atomistic simulation of reference. In this work, instead, we treat the identity for the grand potential based on the thermodynamic relation $Ω=-pV$ and investigate the behaviour of the pressure in the coupling region of the adaptive resolution method (AdResS). We confirm the physical consistency of the method for determining the chemical potential described by the previous work and strengthen it further by identifying a clear numerical relation between the potential that couples the open system to the reservoir on the one hand and the local pressure of the reference fully atomistic system on the other hand. Such a relation is of crucial importance in the perspective of coupling the AdResS method for open system to the continuum hydrodynamic regime.

cond-mat.stat-mech↗

arXiv2021

Nonequilibrium induced by reservoirs: Physico-mathematical models and numerical tests

In a recently proposed computational model of open molecular systems out of equilibrium [Ebrahimi Viand et al. J.Chem.Phys. 153, 101102 (2020)], the action of different reservoirs enters as a linear sum into the Liouville-type evolution equations for the open system's statistics. The linearity of the coupling is common to different mathematical models of open systems and essentially relies on neglecting the feedback of the system onto the reservoir due to their interaction. In this paper, we test the range of applicability of the computational model with a linear coupling to two different reservoirs, which induces a nonequilibrium situation. To this end, we studied the density profiles of Lennard-Jones liquids in large thermal gradients using nonequilibrium molecular dynamics simulations with open boundaries. We put in perspective the formulation of an extension of the mathematical model that can account for nonlinear effects.

cond-mat.stat-mech↗

arXiv2020

Thermodynamic relations at the coupling boundary in adaptive resolution simulations for open systems

The adaptive resolution simulation (AdResS) technique couples regions with different molecular resolutions and allows the exchange of molecules between different regions in an adaptive fashion. The latest development of the technique allows to abruptly couple the atomistically resolved region with a region of non-interacting point-like particles. The abrupt set-up was derived having in mind the idea of the atomistically resolved region as an open system embedded in a large reservoir at a given macroscopic state. In this work, starting from the idea of open system, we derive thermodynamic relations for AdResS which justify conceptually and numerically the claim of AdResS as a technique for simulating open systems. In particular, we derive the relation between the chemical potential of the AdResS set-up and that of its reference fully atomistic simulation. The implication of this result is that the grand potential of AdResS can be explicitly written and thus, from a statistical mechanics point of view, the atomistically resolved region of AdResS can be identified with a well defined open system.

cond-mat.stat-mech↗

arXiv2020

Free energy computation of particles with membrane-mediated interactions via Langevin dynamics

We apply well-established concepts of Langevin sampling to derive a new class of algorithms for the efficient computation of free energy differences of fluctuating particles embedded in a 'fast' membrane, i.e., a membrane that instantaneously adapts to varying particle positions. A geometric potential accounting for membrane-mediated particle interaction is derived in the framework of variational hybrid models for particles in membranes. Recent explicit representations of the gradient of the geometric interaction potential allows to apply well-known gradient based Markov Chain Monte-Carlo (MCDC) methods such as Langevin-based sampling.

math.NA↗

arXiv2020

Liouville-type equations for the n-particle distribution functions of an open system

In this work we derive a mathematical model for an open system that exchanges particles and momentum with a reservoir from their joint Hamiltonian dynamics. The complexity of this many-particle problem is addressed by introducing a countable set of n-particle phase space distribution functions just for the open subsystem, while accounting for the reservoir only in terms of statistical expectations. From the Liouville equation for the full system we derive a set of coupled Liouville-type equations for the n-particle distributions by marginalization with respect to reservoir states. The resulting equation hierarchy describes the external momentum forcing of the open system by the reservoir across its boundaries, and it covers the effects of particle exchanges, which induce probability transfers between the n- and (n+1)-particle distributions. Similarities and differences with the Bergmann-Lebowitz model of open systems (P.G.Bergmann, J.L. Lebowitz, Phys.Rev., 99:578--587 (1955)) are discussed in the context of the implementation of these guiding principles in a computational scheme for molecular simulations.

math-ph↗

arXiv2020

Open Systems out of Equilibrium: Theory and Simulation

We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution molecular dynamics technique (AdResS). We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with results obtained from the simulation of a larger, locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.

cond-mat.stat-mech↗

arXiv2019

Nanoscale domains in ionic liquids: A statistical mechanics definition for molecular dynamics studies

One of the many open questions concerning Ionic Liquids (ILs) is the existence of nanoscale supramolecular domains which characterize the bulk. The hypothesis of their existence does not meet a general consensus since their definition seems to be based on ad hoc arbitrary criteria rather than on general and solid first principles of physics. In this work, we propose a suitable definition of supramolecular domains based on first principles of statistical mechanics. Such principles can be realized through the application of a recently developed computational tool which employs adaptive molecular resolution. The method can identify the smallest region of a liquid for which the atomistic details are strictly required, while the exterior plays the role of a generic structureless thermodynamic reservoir. We consider four different imidazolium-based ILs and show that indeed one can quantitatively represent the liquid as a collection of atomistically self-contained nanodroplets embedded in a generic thermodynamic bath. Such nanodroplets express a characteristic length scale for heterogeneity in ILs.

physics.chem-ph↗