相关论文: Boltzmann and Gibbs: An Attempted Reconciliation
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
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-Planck's principle,…
We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
We present coordinated formulations of local thermodynamical equilibrium conditions at three levels, namely the macroscopic one of classical thermodynamics, the mesoscopic one of hydrodynamical fluctuations and the microscopic one of…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the system in any…
Despite well over a century of effort, the proper expression for the classical entropy in statistical mechanics remains a subject of debate. The Boltzmann entropy (calculated from a surface in phase space) has been criticized as not being…
Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs'…
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 formulate the problem of approach to equilibrium in algebraic quantum statistical mechanics and study some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
Very recently, the validity of the concept of negative temperature has been challenged by several authors since they consider Boltzmann's entropy (that allows negative temperatures) inconsistent from a mathematical and statistical point of…
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,…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…