| Summary: | In this manuscript, we investigate the cosmological and thermodynamic aspects of the Brans–Dicke theory of gravity for a spatially flat FRW universe. We consider a theoretical model for interacting Kaniadakis holographic dark energy with the Hubble horizon as the infrared cutoff. We deal with two interaction scenarios (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Q</mi><mn>2</mn></msub></semantics></math></inline-formula>) between Kaniadakis holographic dark energy and matter. In this context, we study different possible aspects of cosmic evolution through some well-known cosmological parameters such as Hubble <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></semantics></math></inline-formula>, deceleration <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>, jerk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></semantics></math></inline-formula>, and equation of state <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>ω</mi><mi>d</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>. For both interaction terms, it is observed that the deceleration parameter exhibits early deceleration to the current accelerating universe and also lies within the suggested range of Planck data. The equation of state parameter shows quintessence behavior (for the first interaction term) and phantom-like behavior (for the second interaction term) of the universe. The jerk parameter represents consistency with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model for both interaction terms. In the end, we check the thermodynamic behavior of the underlying model. It is interesting to mention here that the generalized second law of thermodynamics holds for both cases of interaction terms.
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