04 - Emergence of Thermodynamics from a Coherence Driven Discrete Informational Framework

This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints.

Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework's effective structures.

The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates.

Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series.

This article derives thermodynamics as the unique coarse-grained consequence of coherence loss within the informational framework established in Papers 01–03.

Starting from the coherence-selected physical sector and its effective quantum description, the work introduces coarse-graining as a constructive mechanism and studies the emergence of irreversible macroscopic behavior from an underlying coherence-preserving dynamics.

The analysis derives entropy as the unique information-loss functional compatible with the structural constraints of the framework, proves the second law as a monotonicity consequence of the induced semigroup evolution, and establishes the relation between quantum coherence reduction and thermodynamic behavior.

Equilibrium, temperature, and thermodynamic potentials are obtained as structural consequences rather than independent postulates.

No thermodynamic laws are assumed at the foundational level. The purpose of the article is to show how thermodynamic structure may emerge as an effective macroscopic description of the same informational dynamics that gives rise to quantum mechanics.