Before Heat: Time as Index and the Structural Origin of Irreversibility

Trilogy Overview: Time as Index and the Landauer Interface (Paper 2 of 3) This paper addresses the origin of irreversibility by distinguishing structural necessity from thermodynamic implementation cost. It provides a resolution to the tension between microscopic reversibility and macroscopic time asymmetry without modifying existing laws. By defining Time as Index and identifying Slip as a deterministic structural residue of bounded non-closed systems, we show that temporal ordering is established "before heat" is invoked. Core Result: Structural irreversibility precedes thermodynamic dissipation. Time is an index before it is a cost. This version is tailored for peers in physics and information theory, focusing on the interface with statistical mechanics.