Thermodynamics and Energy Conditions of Accelerating Brans-Dicke Universe

In this work, we examine the cosmological viability of an accelerating Brans–Dicke universe in the presence of Tsallis holographic dark energy, extending earlier study that employed a logarithmic form of the Brans–Dicke scalar field in a spatially flat Friedmann–Robertson–Walker space–time. While previous analysis has primarily focused on late–time acceleration, we investigate both early and late–time cosmic evolution within this framework. The dynamical behavior of the deceleration and equation–of–state parameters is analyzed to assess whether the model can qualitatively reproduce the known expansion history of the universe, including an inflationary phase and the subsequent decelerated era. We further examine the evolution of the matter to dark energy density ratio and find that it varies sufficiently slowly at late times, indicating a soft alleviation of the cosmic coincidence problem. In addition, the generalized second law of thermodynamics is employed as a consistency test to assess the thermodynamic viability of the model during different evolutionary epochs. The standard energy conditions are also investigated as consistency checks rather than as sources of novel phenomenology. Our results indicate that the considered Tsallis holographic dark energy scenario within Brans-Dicke theory provides a self-consistent and analytically tractable framework for describing the qualitative features of cosmic evolution.