Related papers: Gibbs-Jaynes Entropy Versus Relative Entropy
The dynamics of the expansion of a Lennard-Jones system, initially confined at high density and subsequently expanding freely in the vacuum, is confronted to an expanding statistical ensemble, derived in the diluted quasi-ideal Boltzmann…
For a system moving away from equilibrium, we express the entropy production via a two-point correlation function for any time and any distance from equilibrium. The long-time limit gives the sum of the Lyapunov exponents for a general…
In this paper it is shown that in the case of the given probability distribution or histogram using the Jaynes entropy maximum principle an J- measure of uncertainty (JMU) provides the maximum for a given distribution can be constructed.…
The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum…
We present a new approach to far-from-equilibrium statistical mechanics, based on the concept of generalized entropy, which is a microscopically-defined generalization of Onsager-Machlup functional. In the case when a set of slow…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
A generalization of the Gibbs entropy postulate is proposed based on the BBGKY hierarchy as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every absolutely summable relative…
We prove characterization theorems for relative entropy (also known as Kullback-Leibler divergence), q-logarithmic entropy (also known as Tsallis entropy), and q-logarithmic relative entropy. All three have been characterized axiomatically…
Symbolic relative entropy, an efficient nonlinear complexity parameter measuring probabilistic divergences of symbolic sequences, is proposed in our nonlinear dynamics analysis of heart rates considering equal states. Equalities are not…
Many natural and artificial systems whose range of interaction is long enough are known to exhibit (quasi)stationary states that defy the standard, Boltzmann-Gibbs statistical mechanical prescriptions. For handling such anomalous systems…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
The Gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints. This quantity characterizes the level of order and randomness encoded in features of…
Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies,…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic…
Based on Jaynes' maximum entropy principle, exponential random graphs provide a family of principled models that allow the prediction of network properties as constrained by empirical data (observables). However, their use is often hindered…