
(a) Energy plotted as a function of momentum and for various values of the anisotropy r. Both the branches of matter, E+(p), and antimatter, │E−│(p), are shown. (b) Locus of momentum pmin(r) and energy |E−|min(r), corresponding to the energy minimum for the antimatter, plotted for all anisotropies, 0 ≤ r ≤ 2.
This a novel and broadened theoretical framework of special relativity, which is unified for describing entropies and velocities, and consistent with both thermodynamics and kinematics. The new theory is not to be confused with some relativistic adaptation of thermodynamics; instead, it is a unification of the physical disciplines of thermodynamics and kinematics that surprisingly share an identical description within the framework of relativity.
In the paper, first we show that entropy and velocity are characterized by three identical postulates, which provide the basis of a broader framework of relativity. The postulates lead to a unique form of addition for entropies and for velocities, called kappa-addition. We develop a systematic method of constructing a nonlinear theory of relativity, based on the kappa-addition formulation, that is fully consistent with both thermodynamics and kinematics.
From the generality of the kappa-addition formulation we focus on the cases corresponding to linear adaptations of special relativity. Then, we show how the developed thermodynamic relativity leads to the addition of entropies in nonextensive thermodynamics and the addition of velocities in Einstein’s special relativity, as in two extreme cases, while intermediate cases correspond to a possible anisotropic adaptation of relativity.
Using the thermodynamic relativity for velocities, we start from the kappa-addition of velocities and construct the basic formulations of the linear anisotropic special relativity; e.g., the asymmetric Lorentz transformation, the nondiagonal metric, and the energy-momentum-velocity relationships. Then, we discuss the physical consequences of the possible anisotropy in known relativistic effects, such as, (i) matter-antimatter asymmetry, (ii) time dilation, and (iii) Doppler effect, and show how these might be used to detect and quantify any anisotropy.
See also, the AI-generated interview: https://drive.google.com/file/d/1uwuwVXrTV4TB532etELNghQfuoGZ5-MY/view?usp=drive_link