Related papers: Statistical mechanics of the $N$-queens problem
We review some recent highlights from the applications of statistical-thermal models to different experimental measurements and lattice QCD thermodynamics, that have been made during the last decade. We start with a short review of the…
In recent work Simkin shows that bounds on an exponent occurring in the famous $n$-queens problem can be evaluated by solving convex optimization problems, allowing him to find bounds far tighter than previously known. In this note we use…
The effective potential approach for composite operators is generalized to non-zero temperature in order to derive the non-perturbative analytical equation of state for pure SU(3) Yang-Mills fields valid in the whole temperature range.…
Thermodynamical properties of canonical and grand-canonical ensembles of the half-filled two-site Hubbard model have been discussed within the framework of the nonextensive statistics (NES). For relating the physical temperature $T$ to the…
Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for…
We introduce an exactly solvable lattice model that reveals a universal finite-size scaling law for configurational entropy driven purely by geometry. Using exact enumeration via Burnside's lemma, we compute the entropy for diverse 1D, 2D,…
We study the quantum dynamics of filling an empty lattice of size $L$, by connecting it locally with an equilibrium thermal bath that injects non-interacting bosons or fermions. We adopt four different approaches, namely (i) direct exact…
Generalization through novel interpretations of the inner logic of the century-old Gibbs' statistical thermodynamics is presented: i) Identifying $k_B\to 0$ as classical energetics, one directly derives a pair of thermodynamic variational…
We study nonequilibrium steady states (NESSs) in the weakly-coupled XXZ model in contact with two heat baths at different temperatures. We show that the density matrix can be represented using only projection operators specified by the…
We consider a fermion gas on a star graph modeling a quantum wire junction and derive the entanglement entropy of one edge with respect to the rest of the junction. The gas is free in the bulk of the graph, the interaction being localized…
It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their…
In this article, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated…
A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The R\'enyi entanglement entropy between spatial subregions is explored across the…
We provide here an explicit example of Khinchin's idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics. This point of view is supported by extensive numerical…
Confinement of quarks due to the strong interaction and the deconfinement at high temperatures and high densities are a basic paradigm for understanding the nuclear matter. Their simulation, however, is very challenging for classical…
We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density,…
The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an…
A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases,…
We present a protocol for the study of the dynamics and thermodynamics of quantum systems strongly coupled to a bath and subject to an external modulation. Our protocol quantifies the evolution of the system-bath composite by expanding the…
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the…