[Paper Review] A general concept of natural information equilibrium: from the ideal gas law to the K-Trumpler effect

P. Fielitz, G. Borchardt|arXiv (Cornell University)|May 5, 2009

Advanced Thermodynamics and Statistical Mechanics2 references3 citations

TL;DR

This paper introduces a generalized concept of natural information equilibrium that eliminates the need for arbitrary constraints in information theory, enabling direct application to non-physical and far-from-equilibrium systems. It demonstrates the framework using the ideal gas law and stellar diffusion, successfully quantifying the K-Trumpler effect through a physically meaningful, system-independent measure of information.

ABSTRACT

Information theory provides shortcuts which allow one to deal with complex systems. The basic idea one uses for this purpose is the maximum entropy principle developed by Jaynes. However, an extension of this maximum entropy principle to systems far from thermodynamic equilibrium or even to non-physical systems is problematic because it requires an adequate choice of constraints. In this paper we discuss a general concept of natural information equilibrium which does not require any choice of adequate constraints. It is, therefore, directly applicable to systems far from thermodynamic equilibrium and to non-physical systems/processes (e.g. biological processes and economical processes). We demonstrate the validity and the applicability of the concept by three well understood physical processes. As an interesting astronomical application we will show that the concept of natural information equilibrium allows one to rationalize and to quantify the K-Trumpler effect.

Motivation & Objective

• To develop a system- and process-independent framework for information equilibrium that does not require subjective constraint selection.
• To address limitations of the maximum entropy principle in non-equilibrium and non-physical systems such as biological and economic processes.
• To provide a physically grounded, natural definition of information that avoids the pitfalls of traditional information theory in degenerate cases (e.g., s=1).
• To demonstrate the framework’s validity using well-understood physical systems like diffusion and the ideal gas law.
• To apply the model to the K-Trumpler effect, offering a quantitative, phenomenological explanation previously lacking in astrophysics.

Proposed method

• Defines a 'natural amount of information' based on a generic process variable, ensuring physical relevance even in extreme or degenerate cases.
• Applies the information equilibrium condition Ix = Iy (information source equals information destination) as a fundamental equilibrium state.
• Uses the information transfer equation (I_x = κ I_y) to model systems where information flows between variables without loss.
• Derives the K-Trumpler effect from the information equilibrium framework by modeling stellar opacity and light extinction as information transfer processes.
• Validates the model using the diffusion equation and ideal gas law, showing consistency with known physical laws.
• Replaces abstract detector models with direct physical interpretation of information transfer in astrophysical contexts.

Experimental results

Research questions

• RQ1 How can information equilibrium be defined in a way that is independent of arbitrary constraints, especially in non-physical systems?
• RQ2 Can the concept of natural information equilibrium explain the K-Trumpler effect without relying on ad hoc assumptions?
• RQ3 Why do traditional information theory measures fail in degenerate cases (e.g., s=1), and how can this be resolved?
• RQ4 How does the natural amount of information relate to measurable physical quantities in diffusion and gas laws?
• RQ5 Can information equilibrium serve as a unifying principle across diverse systems, from thermodynamics to astrophysics?

Key findings

• The natural amount of information, defined via a generic process variable, provides a physically meaningful and system-independent measure of information, resolving failures of traditional information theory in degenerate cases.
• The information equilibrium condition Ix = Iy allows for direct modeling of complex systems without requiring prior selection of constraints.
• The K-Trumpler effect is successfully rationalized and quantified using the natural information equilibrium framework, offering a new phenomenological explanation for interstellar extinction.
• The model reproduces the ideal gas law and diffusion processes by treating physical laws as manifestations of information equilibrium, validating its consistency with established physics.
• The framework eliminates the need for abstract detectors in astrophysical modeling by directly linking information transfer to observable physical quantities like tracer diffusion and stellar opacity.
• The information transfer constant κz is shown to be experimentally determinable and process-specific, grounding the abstract concept in empirical reality.