Related papers: Relativistic Roots of $\kappa$-Entropy
In the present effort we show that $S_{\kappa}=-k_B \int d^3p (n^{1+\kappa}-n^{1-\kappa})/(2\kappa)$ is the unique existing entropy obtained by a continuous deformation of the Shannon-Boltzmann entropy $S_0=-k_B \int d^3p n \ln n$ and…
The Lesche stability condition for the Shannon entropy [B. Lesche, J. Stat. Phys. 27, 419 (1982)], represents a fundamental test, for its experimental robustness, for systems obeying the Maxwell-Boltzmann statistical mechanics. Of course,…
We have investigated the proof of the $H$ theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [Phy. Rev. E {\bf 66}, 056125, 2002; {\it ibid.} {\bf 72}, 036108 2005]. In our…
In special relativity the mathematical expressions, defining physical observables as the momentum, the energy etc, emerge as one parameter (light speed) continuous deformations of the corresponding ones of the classical physics. Here, we…
The Heisenberg position-momentum uncertainty relation is a cornerstone of quantum mechanics. However, its standard formulation is not fully consistent with special relativity. While partial understanding has been achieved in the…
Kaniadakis ($\kappa$-deformed) statistics is being widely used for describing relativistic systems with non-extensive behavior and/or interactions. It is built upon a one-parameter generalization of the classical Boltzmann-Gibbs-Shannon…
We show that the principle of entropy increase may be exactly founded on a few axioms valid not only for quantum and classical statistics, but also for a wide range of statistical processes.
The intriguing and still open question concerning the composition law of $\kappa$-entropy $S_{\kappa}(f)=\frac{1}{2\kappa}\sum_i (f_i^{1-\kappa}-f_i^{1+\kappa})$ with $0<\kappa<1$ and $\sum_i f_i =1$ is here reconsidered and solved. It is…
Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…
It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fix univocally the entropy of the system, which turn out to be the Boltzmann-Gibbs-Shannon…
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…
A theory of the cosmological constant Lambda is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the…
(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
Adopting a bottom-up perspective, we propose a novel two-parametric nonadditive entropy, $S_{\kappa\ell}$, associated with a Kappa-type power-law velocity distribution, $F_{\kappa\ell}(v)$, recently derived in the literature. By formulating…
The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann-Gibbs (BG) entropy and are…
We have investigated the proof of the $H$ theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phy. Rev. E {\bf 66}, 056125, 2002; {\it ibid.} {\bf 72}, 036108,…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…