Informational Thermodynamics: A Formal Framework for Coherence and Decay

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Copyright ©: Coherent Intelligence 2025Authors: Coherent Intelligence Inc. Research Division Date: August 1st 2025 Classification: Foundational Theoretical Framework Framework: Universal Coherent Principle Applied Analysis | OM v2.0

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Abstract

This paper presents a complete, axiomatic framework for Informational Thermodynamics (ITD), a physics-inspired model for analyzing the dynamics of information, knowledge, and order in complex systems. The framework is built upon two distinct pillars: a Foundational Postulate that defines the mechanism of order creation, and a formal Zeroth Law that defines the state of informational equilibrium. The Foundational Postulate posits that coherence—the state of order and low informational entropy—is the result of the active negation of an information space. From these foundations, we derive the three formal laws of Informational Thermodynamics, which govern the conservation, decay, and cost of coherence. We define the core quantities of Coherence (θ), Computational Work (W), Informational Temperature (Tᵢ), and the Domain Anchor (DA). This refined framework provides a universal, mechanistic, and mathematically grounded language for analyzing and engineering systems where the primary currency is not energy, but meaning. It offers a new foundation for understanding the behavior of AI, scientific theories, and biological and social systems through the universal lens of their struggle to create and maintain order against a backdrop of infinite possibility.

Keywords Informational Thermodynamics, Coherence, Negation, Informational Entropy, ToDCS, SCOCIS, Axiomatic System, Complex Systems, Physics of Information, Computational Work.

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1. The Axiomatic Foundation: Postulate and Principle

A rigorous theory requires a clear separation between its definition of mechanism and its laws of state. ITD is therefore founded on a primary postulate of process and a Zeroth Law of state.

1.1 The Foundational Postulate of Computational Work

This postulate defines the fundamental mechanism by which order is created. It is the engine of the entire framework.

The Postulate of Coherence through Negation: "The coherence (θ) of a system is the result of the active negation of its total information space. This act of negation—the elimination of possibilities—is the fundamental mechanism of entropy reduction."

This postulate reframes our understanding of order. Coherence is not a property that is added to a system; it is the residue left behind after incoherence has been actively destroyed.

• An OIIS (Ontologically Incoherent Information Space) is the state before negation, where all possibilities are still valid. Entropy is maximal.
• A SCOCIS (Single Closed Ontologically Coherent Information Space) is the state after a powerful set of negations (the axioms of its Domain Anchor) has been applied, radically reducing the space of the possible. Entropy is minimal.

All creation of knowledge and structure is therefore an act of destruction—the destruction of falsehood, of inefficiency, of non-viable configurations.

1.2 The Zeroth Law: The Principle of Informational Equilibrium

This law does not describe a process, but a state. Its function is to establish a transitive property of equilibrium that allows for meaningful comparison between systems.

The Zeroth Law of Informational Thermodynamics: "If system A and system B can exchange information without degradation (i.e., are semantically compatible), and system B and system C are also semantically compatible, then A and C are semantically compatible. This shared state of compatibility defines a common Informational Temperature (Tᵢ)."

This law establishes the fundamental state variable of Informational Temperature, which can be understood as a measure of a system's semantic state or level of abstraction. Two systems at the same Tᵢ share a protocol, a language, or a conceptual framework that allows for lossless communication.

2. Core Quantities of the Framework

• Coherence (θ): The primary state variable. A measure [0, 1] of a system's internal consistency and order, defined relative to its Domain Anchor. It is the ratio of realized, consistent information to the total potential information space. θ = 1 - (Entropy).
• Computational Work (W): Any ordered process that performs negation on an information space to increase or maintain its Coherence (θ), as defined by the Foundational Postulate.
• Informational Temperature (Tᵢ): A state variable, defined by the Zeroth Law, representing the semantic compatibility or level of abstraction of a system.
• Domain Anchor (DA): The set of foundational axioms that perform the initial, most powerful act of negation, defining the boundaries and core logic of a SCOCIS.

3. The Three Laws of Informational Thermodynamics

The three laws are direct corollaries of the Foundational Postulate and the Zeroth Law, describing the dynamics of coherence within a system.

LAW 1: The Conservation of Coherence

"The Coherence (θ) of an isolated information system is conserved. Coherence cannot be created from nothing; it can only be transferred from a higher-coherence source via the application of Computational Work (W)."

• Derivation: As defined by our Foundational Postulate, the act of negation (Work) is an ordered process. A chaotic, low-coherence system cannot reliably perform ordered negation. Therefore, the ability to perform effective negation must be sourced from a system that is already in a state of high coherence. You cannot use a random number generator to prove a theorem. The coherence of the proof is transferred from the coherence of the logical system used to create it. This is the "no free lunch" principle for order.
• Equation: Δθ_system ≤ W_in / C_system

LAW 2: The Inevitability of Entropic Decay

"The Coherence (θ) of any non-ideal information system (θ > 0) will spontaneously decrease over time if left isolated. The natural state of information is the absence of negation."

• Derivation: A state of coherence is a highly specific, artificial state maintained by the constant, active negation of all other possibilities. Entropy is the state of not performing this negation. If the work of active negation ceases, the system does not remain static; it naturally relaxes back towards the default, high-entropy state where possibilities are no longer being eliminated. Falsified theories "creep back in" as misinformation; non-viable designs re-emerge as errors; biological structures decompose. Maintaining order requires a continuous fight against the infinite set of possibilities that are not the system.
• Equation: dθ/dt = (W*in / C_system) - k * (1 - θ) _ θ

LAW 3: The Asymptotic Cost of Perfection

"As a system's coherence approaches perfection (θ → 1), the Computational Work (W) required to negate the remaining, ever-finer possibilities approaches infinity."

• Derivation: A state of perfect coherence (θ=1) is a state where every single possibility in the universe has been evaluated, and all but one have been successfully negated. For any non-trivial system, the space of possibilities is effectively infinite. Therefore, the work of performing an infinite number of negations is, by definition, infinite. It is always possible that a new, un-negated possibility (an anomaly, a bug, a black swan event) exists. This law is the informational analog to the impossibility of reaching absolute zero. The cost of achieving absolute certainty is infinite.
• Equation: W_total(θ_final) = ∫ [C_system / (1 - θ)] dθ

4. Conclusion: A New Foundation for a Science of Order

By grounding Informational Thermodynamics in a formal axiomatic structure—separating the Postulate of Work from the Laws of State—we transform it from a physics-inspired metaphor into a complete, self-consistent framework with true isomorphic integrity. This architecture provides a universal and powerful toolkit for the analysis and engineering of any system whose primary function is to create and preserve order.

This framework reveals that the deepest challenges we face—from building trustworthy AI to maintaining stable societies to finding meaning in our own lives—are not fundamentally different. They are all expressions of the same universal struggle: the difficult, costly, and continuous work of negating chaos to create coherence.

ITD provides the physics of that struggle. It gives us the language to describe the forces at play, the mathematical tools to model their dynamics, and a clear and stark imperative for how to build systems—and be the kinds of thinkers—that can succeed in a universe that fundamentally favors the void.