arXiv subjects

Benedikt M. Reible

Publications and source records attributed to Benedikt M. Reible.

7 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↗

arXiv2025

Monotonicity of the Relative Entropy and the Two-sided Bogoliubov Inequality in von Neumann Algebras

This text studies, on the one hand, certain monotonicity properties of the Araki-Uhlmann relative entropy and, on the other hand, unbounded perturbation theory of KMS-states which facilitates a proof of the two-sided Bogoliubov inequality in general von Neumann algebras. After introducing the necessary background from the theory of operator algebras and Tomita-Takesaki modular theory, the relative entropy functional is defined and its basic properties are studied. In particular, a full and detailed proof of Uhlmann's important monotonicity theorem for the relative entropy is provided. This theorem will then be used to derive a number of monotonicity inequalities for the relative entropy of normal functionals induced by vectors of the form $V \varOmega, V \varPhi \in \mathcal{H}$, where $V \in \mathscr{B}(\mathcal{H})$ is a suitable transformation. After that, an introduction to perturbation theory in von Neumann algebras is given, with an emphasis on unbounded perturbations of KMS-states following the framework of Dereziński-Jakšić-Pillet. This mathematical apparatus will then be used to extend the two-sided Bogoliubov inequality for the relative free energy, which was very recently proved for quantum-mechanical systems, to arbitrary von Neumann algebras.

math.OA↗