Related papers: A statistical perspective on microsolvation
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann's principle,…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
I present a theoretical model of a quantum statistical ensemble for which, unlike in conventional physics, the total number of particles is extremely small. The thermodynamical quantities are calculated by taking a small $N$ by virtue of…
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard…
Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient relaxation algorithms…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
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…
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…
We exploit a prescription to observe directly the physical properties of the thermodynamic limit under continuously applied field in one-dimensional quantum finite lattice systems. By systematically scaling down the energy of the…
We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a…
The formation and dissolution of a droplet is an important mechanism related to various nucleation phenomena. Here, we address the droplet formation-dissolution transition in a two-dimensional Lennard-Jones gas to demonstrate a consistent…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
We consider a small Hamiltonian system strongly interacting with a much larger Hamiltonian system (the bath), while being driven by both a time-dependent control parameter and non-conservative forces. The joint system is assumed to be…
We reconsider some general aspects about the mean field thermodynamical description of the astrophysical systems based on the microcanonical ensemble. Starting from these basis, we devote a special attention to the analysis of the scaling…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
A model for the thermodynamics of a quantum heat bath is introduced. Under the assumption that the bath molecules have finitely many degrees of freedom and are weakly interacting, we present a general derivation of the equation of state of…
Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…