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In this paper, we investigate the anisotropic and spatially homogeneous Bianchi type-I universe with Kaniadakis holographic dark energy in Saez–Ballester [Phys. Lett. A 113, 467 (1986)] theory of gravitation. We determine Kaniadakis holographic dark energy model by assuming a correlation between the metric potentials to solve the field equations of the model. This results in a dynamical deceleration parameter which demonstrates an accelerating expansion of the universe. Our model’s equation of state parameter [Formula: see text] close to [Formula: see text] ([Formula: see text] model) at late-times and is in agreement with the most recent observations. Next, we obtained the squared sound speed ([Formula: see text]) and found that it is positive, implying stability against perturbations. The [Formula: see text] plane is constructed to investigate the evolution of the models’ EoS parameter turned out to be in a freezing zone. As should be the case in an expanding universe, the strong energy conditions of the model are violated. Statefinders [Formula: see text], and [Formula: see text] planes were also examined. Our model includes the Chaplygin gas, [Formula: see text] limit, and is inclined towards the steady-state model.
In this paper, we investigate the anisotropic and spatially homogeneous Bianchi type-I universe with Kaniadakis holographic dark energy in Saez–Ballester [Phys. Lett. A 113, 467 (1986)] theory of gravitation. We determine Kaniadakis holographic dark energy model by assuming a correlation between the metric potentials to solve the field equations of the model. This results in a dynamical deceleration parameter which demonstrates an accelerating expansion of the universe. Our model’s equation of state parameter [Formula: see text] close to [Formula: see text] ([Formula: see text] model) at late-times and is in agreement with the most recent observations. Next, we obtained the squared sound speed ([Formula: see text]) and found that it is positive, implying stability against perturbations. The [Formula: see text] plane is constructed to investigate the evolution of the models’ EoS parameter turned out to be in a freezing zone. As should be the case in an expanding universe, the strong energy conditions of the model are violated. Statefinders [Formula: see text], and [Formula: see text] planes were also examined. Our model includes the Chaplygin gas, [Formula: see text] limit, and is inclined towards the steady-state model.
The axiomatic structure of the κ-statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the κ-entropy and its special limiting case, the classical Boltzmann–Gibbs–Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from κ-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the κ-formalism, which emerges from the κ-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on κ-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the κ-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized.
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