Related papers: Gibbs Entropy and Irreversibility
Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned…
Boltzmann introduced in the 1870's a logarithmic measure for the connection between the thermodynamical entropy and the probabilities of the microscopic configurations of the system. His entropic functional for classical systems was…
Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{BG}=-k \sum_{i=1}^W p_i \ln p_i$. It enables a successful thermal approach of ubiquitous systems, such as those involving short-range interactions, markovian processes, and,…
The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy…
The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics. This problem was considered by Boltzmann, Poincar\'e, Bogolyubov and many other authors and though some…
Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the…
We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the…
We consider the kinetic theory of dilute gases in the Boltzmann--Grad limit. We propose a new perspective based on a large deviation estimate for the probability of the empirical distribution dynamics. Assuming Boltzmann molecular chaos…
We establish the irreversibility of renormalization group flows on a pointlike defect inserted in a $d$-dimensional Lorentzian conformal field theory. We identify the impurity entropy $g$ with the quantum relative entropy in two equivalent…
In the second half of the 19th century, the kinetic theory of gases has probably raised one of the most impassioned debates in the history of science. The so-called reversibility paradox around which intense polemics occurred reveals the…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on the additive entropy $S_{BG}=- k_B\sum_{i=1}^W p_i \ln p_i$. Its optimization under appropriate…
The critique against using Boltzmann's microcanonical entropy, an "ensemble measure", as foundation of statistics is rebuffed. The confusion of the microcanonical distribution with the exponential Boltzmann-Gibbs (``BG'') distribution is…
We study Poincar\'e recurrence from a purely geometrical viewpoint. We prove that the metric entropy is given by the exponential growth rate of return times to dynamical balls. This is the geometrical counterpart of Ornstein-Weiss theorem.…
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…
Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are considered. The basic structure of the statistical hypersurface…
Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…
Understanding irreversibility in macrophysics from reversible microphysics has been the holy grail in statistical physics ever since the mid-19th century. Here the central question concerns the arrow of time, which boils down to deriving…
A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states…
In this article, we prove the Eyring-Kramers formula for non-reversible metastable diffusion processes that have a Gibbs invariant measure. Our result indicates that non-reversible processes exhibit faster metastable transitions between…