Time asymmetry in thermodynamic systems, governed by the Second Law of Thermodynamics, has long been associated with the natural progression toward equilibrium, although interpretations vary widely across scientific perspectives. To address this diversity, a more comprehensive framework that encompasses both equilibrium and non-equilibrium states is essential. This paper introduces the Minus First Law as a foundational principle to expand the thermodynamic framework and more effectively account for time asymmetry. The concept enables an analysis of both symmetrical and asymmetrical states across forward and reverse temporal directions, addressing the complex interplay between the thermodynamic arrow of time and the statistical mechanics arrow. By broadening the theoretical scope, it aims to bridge gaps across macroscopic and microscopic scales, offering a unified perspective on time asymmetry within both equilibrium and non-equilibrium thermodynamic systems. Such an approach could refine our understanding of irreversible processes and deepen insights into the emergence of temporal asymmetry from microscopic dynamics.