  Understanding the evolution of entropy in the universe is a fundamental
aspect of cosmology. This paper investigates the evolution of entropy in a
spatially flat $K=0$ universe, focusing on the contributions of matter,
radiation, and dark energy components. The study derives the rate of change of
entropy with respect to cosmic time, taking into account the scaling relations
of energy densities and temperatures for different components. The analysis
reveals the dominance of radiation entropy at early times, transitioning to
matter dominance as the universe expands. The constant contribution of dark
energy entropy throughout cosmic time is also considered. The paper
acknowledges the limitations of the simplified model and the omission of
entropy generation processes, emphasizing the importance of future research to
incorporate these aspects. The results highlight the complex interplay between
different components and provide insights into the dynamics of entropy in the
expanding universe. This study lays the foundation for further investigations
into entropy evolution, urging the consideration of more comprehensive models
and numerical techniques to achieve a deeper understanding of the universe's
thermodynamic behavior.
