Related papers: On the dispute between Boltzmann and Gibbs entropy
We study the dynamic and thermodynamic origin of non-canonical equilibria, and we discuss their connection with the generalized central limit theorem and the micro-canonical Boltzmann principle. We reach the conclusion that the zeroth law…
We study the equilibrium simplex of Nica-Pimsner algebras arising from product systems of finite rank on the free abelian semigroup. First we show that every equilibrium state has a convex decomposition into parts parametrized by ideals on…
Boltzmann's microcanonical entropy is the link between statistical physics and thermodynamics, forasmuch as the behavior of any thermodynamic quantity is directly related to the number of microscopic configurations. Accordingly, in this…
Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several…
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body…
We show how to generalise the zero temperature Lanczos method for calculating dynamical correlation functions to finite temperatures. The key is the microcanonical ensemble, which allows us to replace the involved canonical ensemble with a…
We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short…
We analyze the statistical mechanics of a gas of neutral and charged black holes. The microcanonical ensemble is the only possible approach to this system, and the equilibrium configuration is the one for which most of the energy is carried…
Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multi-phase fluid systems. However, the underlying second order analysis of the equation of motion has long been known to be insufficient to…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
The Boltzmann-Gibbs-von Neumann entropy of a large part (of linear size L) of some (much larger) d-dimensional quantum systems follows the so-called area law (as for black holes), i.e., it is proportional to $L^{d-1}$. Here we show, for…
The theory of small-system thermodynamics was originally developed to extend the laws of thermodynamics to length scales of nanometers. Here we review this "nanothermodynamics," and stress how it also applies to large systems that subdivide…
The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from…
Consistency constraints for low-energy theories, especially those lacking Lorentz invariance, have recently garnered attention. Building on results from black hole thermodynamics, we investigate the conjecture that leading irrelevant…
A way to construct Boltzmann entropy, i.e., the entropy as a function of a microscopic pure state, for quantum field systems is proposed. Operators that shift the field in wavevector space are used in the construction. By employing an…
This study investigates the implications of adopting fractional entropy in the area law framework and demonstrates its natural alignment with an isothermal description of black hole composition. We discuss the Zeroth law compatibility of…
We predict negative temperature states in the Discrete Nonlinear Sch\"odinger equation as exact solutions of the associated Wave Kinetic equation. Those solutions are consistent with the classical thermodynamics formalism. Explicit…
We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each…
We summarize recent results on positive temperature equilibrium states of large bosonic systems. The emphasis will be on the connection between bosonic grand-canonical thermal states and the (semi-) classical Gibbs measures on one-body…
We investigate numerically the low temperature equilibration of glassy systems via non-local Monte Carlo methods. We re-examine several systems that have been studied previously and investigate new systems in order to test the performance…