Planck radiation law and Einstein coefficients reexamined in Kaniadakisκstatistics

Abstract

Blackbody radiation is reconsidered using the counterpart of the Bose-Einstein distribution in the κ statistics arising from the Kaniadakis entropy. The generalized Planck radiation law is presented and compared to the usual law, to which it reduces in the limiting case κ→0. Effective Einstein's coefficients of emission and absorption are defined in terms of the Kaniadakis parameter κ. It is shown that the Kaniadakis statistics keeps unchanged the first Einstein coefficient A while the second coefficient B admits a generalized form within the present theoretical framework.

The validity of the third law of thermodynamics for the Rényi and homogeneous entropies

“…Concerning the question whether any information-theoretic entropy can be useful for constructing a generalized statistical mechanics, many candidates such as the Tsallis [1], Rényi [2], Kaniadakis [3] and homogeneous entropies [4][5][6] have recently been proposed. These generalized entropies have been applied to various fields of research such as quantum information [7][8][9][10], econophysics [11,12], high energy phenomenology [13] and black hole thermodynamics [14,15]. All these entropy definitions share the common feature that they yield distributions of inverse power law type under the entropy maximization [1,3,16,17].…”

Group theory, entropy and the third law of thermodynamics

“…These generalized entropies aim to explain the non-equilibrium stationary metastable states through the deformation in the underlying entropic structure. Along this direction, many important applications were reported in the fields of generalized reaction rates [4][5][6][7], quantum information [8][9][10][11][12][13][14], plasma physics [15][16][17], high energy physics [18][19][20] and the rigid rotators in modelling the molecular structure [21,22]. The common feature of these entropies is to yield inverse power law distributions through the entropy maximization [1,3,23,24].…”

Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle

“…For this reason, it has attracted the interest of many researchers over the last 16 years, who have studied its foundations and mathematical aspects [5][6][7][8][9][10][11][12], the underlying thermodynamics [13][14][15][16][17], and specific applications of the theory in various scientific and engineering fields. A non-exhaustive list of application areas includes quantum statistics [18][19][20], quantum entanglement [21,22], plasma physics [23][24][25][26][27], nuclear fission [28], astrophysics [29][30][31][32][33][34][35], geomechanics [36], genomics [37], complex networks [38,39], economy [40][41][42][43] and finance [44][45][46][47].…”