Discuss the theoretical principles and implications of the second law of thermodynamics within the context of isolated systems. Specifically, analyze how this law governs the direction of spontaneous processes and the concept of entropy, addressing how these principles apply to the theoretical limits of energy conversion and efficiency. Further, explore the philosophical implications of entropy increase as it relates to the notion of the "arrow of time" and its impact on the predictability and reversibility of physical systems at a macroscopic scale. How do these theoretical constructs interplay with the foundations of statistical mechanics, and what are the broader implications for our understanding of natural processes in an idealized universe devoid of any external influences?