Related papers: Statistical mechanics of the $N$-queens problem
Here we investigate how local properties of particles in a thermal bath influence the thermodynamics of the bath. We utilize nanothermodynamics, based on two postulates: that small systems can be treated self-consistently by coupling to an…
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the average von Neumann entropy per site converges to the logarithm…
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative…
We study the Poisson-Boltzmann equation in the context of dense charged fluids where steric effects become important. We generalise the lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare…
The thermodynamic problem of a gas of static quarks carrying U(N) charges and interacting with each other via U(N) electric gauge fields is formulated and solved in the large N limit. In a lattice theory, the solution can be found in any…
A new approach to study the equation of state in finite-temperature QCD is proposed on the lattice. Unlike the conventional method in which the temporal lattice size $N_t$ is fixed, the temperature $T$ is varied by changing $N_t$ at fixed…
We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a…
We study the complexity of finding the ground state energy density of a local Hamiltonian on a lattice in the thermodynamic limit of infinite lattice size. We formulate this rigorously as a function problem, in which we request an estimate…
We consider optimizations of Lenoir heat engine within a quantum dynamical field consisting of $N$ noninteracting fermions trapped in multilevel infinite potential square-well. Fermions play role as working substance of the engine with each…
Periodic driving is used to steer physical systems to unique stationary states or nonequilibrium steady states (NESS), producing enhanced properties inaccessible to non-driven systems. For open quantum systems, characterizing the NESS is…
Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to…
We study the statistical mechanics of the self-gravitating gas at thermal equilibrium with two kinds of particles. We start from the partition function in the canonical ensemble which we express as a functional integral over the densities…
We study the statistics of the kinetic (or equivalently potential) energy for $N$ non-interacting fermions in a $1d$ harmonic trap of frequency $\omega$, at finite temperature $T$. Remarkably, we find an exact solution for the full…
We consider a quantum quench in a non-interacting fermionic one-dimensional field-theory. The system of size $L$ is initially prepared into two halves $\mathcal{L}$ ($[-L/2,0]$) and $\mathcal{R}$ ($[0,L/2]$), each of them thermalized at two…
We present a four-dimensional equation of state for strongly interacting matter at finite temperature and conserved charge densities, constructed using a deep neural network. It is designed for direct use in hybrid models of relativistic…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
Adsorbed gases within, or outside of, carbon nanotubes may be analyzed with an approximate model of adsorption on lattice sites situated on a cylindrical surface. Using this model, the ground state energies of alternative lattice structures…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
The role of the algebraic method has long been understood in shedding light on the topological structure of sets. However, when the set is a simplicial complex and host to a dynamical process, in particular the trajectory of a canonically…
We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential.…