Related papers: Lorentzian Entropies and Olbert's $\kappa$-distrib…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
The kappa distribution of velocities appears routinely in the study of collisionless plasmas present in Earth's magnetosphere, the solar wind among other contexts where particles are unable to reach thermal equilibrium. Originally justified…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…
In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…
The standard (non-relativistic) $\kappa$-distribution is widely used to fit data and to describe macroscopic thermodynamical behavior, e.g.\ the pressure (temperature) as the second moment of the distribution function. By contrast to a…
Certain thermal non-equilibrium situations, outside of the astrophysical realm, suggest that entropy production extrema, instead of entropy extrema, are related to stationary states. In an effort to better understand the evolution of…
Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…
Classical-like formulas are given in order to evaluate thermal averages of observables belonging to a quantum nonlinear system with dissipation described by the Caldeira-Leggett model [Phys. Rev. Lett. 46, 211 (1981); Ann. Phys. (N.Y.) 149,…
For collisionless (or collision-poor) plasma populations which are well described by the $\kappa$-distribution functions (also known as the Kappa or Lorentzian power-laws) a macroscopic interpretation has remained largely questionable,…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
The generally accepted representation of $\kappa$-distributions in space plasma physics allows for two different alternatives, namely assuming either the temperature or the thermal velocity to be $\kappa$-independent. The present paper aims…
The departure of particle distributions from the Maxwellian is commonly observed in space plasmas. These non-Maxwellian distributions which are typical for plasmas that are not in thermal equilibrium, can be modeled with…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and…
A non-relativistic Fokker-Planck equation for the electron distribution function is formulated incorporating the effects of stochastic acceleration by whistler-mode waves and Coulomb collisions. The stationary solution $f$ to the equation,…
The apparent thermalization of the particles produced in hadronic collisions can be obtained by quantum entanglement of the partons of the initial state once a fast hard collision is produced. The scale of the hard collision is related to…
Possible entropy constraints on particle acceleration spectra are discussed. Solar flare models invoke a variety of initial distributions of the primary energy release over the particles of the flare plasma -- ie., the partition of the…
The recently developed concept of "entropic defect" is important for understanding the foundations of thermodynamics in space plasma physics, and more generally, for systems with physical correlations among their particles. Using this…
We study the entropy production in non-equilibrium quantum systems without dissipation, which is generated exclusively by the spontaneous breaking of time-reversal invariance. Systems which preserve the total energy and particle number and…