相关论文: Boltzmann and Gibbs: An Attempted Reconciliation
Aspects of the modern dynamical systems approach to thermodynamics of stationary states out of equilibrium with attention to the original conceptions which arose at the beginnings of Statistical Mechanics
Boltzmannian statistical mechanics partitions the phase space of a system into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann's combinatorial…
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…
Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probability {\it a priori} where thermodynamic infinite-size limit is replaced by multiple-measurement limit. A duality symmetry between Massieu's…
Computer simulations generate trajectories at a single, well-defined thermodynamic state point. Statistical reweighting offers the means to reweight static and dynamical properties to different equilibrium state points by means of analytic…
For classical discrete systems under constant composition, a set of microscopic state dominantly contributing to thermodynamically equilibrium structure should depend on temperature and energy through Boltzmann factor, exp(-bE). Despite…
What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we…
We give a pedagogical introduction to a selection of recently discussed topics in nonequilibrium statistical mechanics, concentrating mostly on formal structures and on general principles. Part I contains an overview of the formalism of…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
In this lecture we briefly review the definition, consequences and applications of an entropy, $S_q$, which generalizes the usual Boltzmann-Gibbs entropy $S_{BG}$ ($S_1=S_{BG}$), basis of the usual statistical mechanics, well known to be…
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis,…
A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational…
For classical systems, expectation value of macroscopic property in equilibrium state can be typically provided through thermodynamic (so-called canonical) average, where summation is taken over possible states in phase space (or in…
Inter-level connections in science routinely require constructs that neither of the connected theories contains. Statistical mechanics requires assumptions such as the Stosszahlansatz to generate thermodynamic irreversibility - assumptions…
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the…
Granular and nanoscale materials containing a relatively small number of constituents have been studied to discover how their properties differ from their macroscopic counterparts. These studies are designed to test how far the known…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…
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…