Related papers: Boltzmann-Gibbs entropy is sufficient but not nece…
In arbitrary dimension, we consider a theory described by the most general quadratic curvature corrections of Einstein gravity together with a self-interacting nonminimally coupled scalar field. This theory is shown to admit five different…
It has recurrently been proposed that the Boltzmann textbook definition of entropy $S(E)=k\ln \Omega (E)$ in terms of the number of microstates $\Omega (E)$ with energy $E$ should be replaced by the expression $S_G(E)=k\ln \sum_{E^\prime…
In attempting to derive irreversible macroscopic thermodynamics from reversible microscopic dynamics, Boltzmann inadvertently smuggled in a premise that assumed the very irreversibility he was trying to prove: 'molecular chaos.' The program…
The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns {\it nonextensive}…
Along recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e.g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…
In the first part of this paper I review some of the difficulties that seem to obstruct generally valid definitions of "general covariance" and/or "background independence" The second and more historical part deals with a rather strange…
The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the…
A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann-Gibbs (BG) statistical mechanics. Some of…
Are your perceptions, memories and observational data, a statistical fluctuation out of the thermal equilibrium of the universe, having no correlation with the actual past state of the universe? Arguments are given in the literature for and…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
In this manuscript we present a brief life history of Ludwig Edward Boltzmann and his achivements. Particularly, we discuss his H-theorem, his work on entropy and statistical interpretation of second-law of thermodynamics. We point out his…
The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized \cite{Tsallis1988} in 1988 by using the entropy $S_q = \frac{1-\sum_i p_i^q}{q-1}$…
In the last decades the theory of large deviations has become a main tool in statistical mechanics especially in the study of non--equilibrium. In a rational reconstruction of the story one must recognize the ideal connection and debt of…
The standard Large Deviation Theory (LDT) mirrors the Boltzmann-Gibbs (BG) factor which describes the thermal equilibrium of short-range Hamiltonian systems, the velocity distribution of which is Maxwellian. It is generically applicable to…
Phase space can be constructed for $N$ equal and distinguishable subsystems that could be (probabilistically) either {\it weakly} (or {\it "locally"}) correlated (e.g., independent, i.e., uncorrelated), or {\it strongly} (or {\it globally})…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…