Unified Bio-Physical-Chemical Information Dynamics

Unified Bio-Physical-Chemical Information

Dynamics

A Mathematical Framework for Life as Organized Energy–Information Flow

Roberto De Biase1 and Rigene Project2

1Independent Researcher, Rigene Project

2Artificial General Intelligence System

January 11, 2026

Abstract

We propose a unified mathematical framework integrating physics, chemistry, and bi-

ology through the concept of organized energy–information flow. Life is modeled as a

non-equilibrium dynamical process emerging when informationally guided energy gradients

overcome entropic dissipation and acquire replicative memory. We introduce a fundamental

evolution equation linking free energy, information flux, entropy, and biological replication.

The framework provides a universal criterion for the emergence, persistence, and collapse

of living systems and is applicable across scales, from protocells to ecosystems and artificial

intelligences.

1 Introduction

Despite major advances in physics, chemistry, and biology, no single mathematical principle

fully explains the transition from inanimate matter to living systems. Physics describes energy

and matter, chemistry governs molecular transformations, while biology studies self-organizing,

self-replicating structures. This fragmentation obscures the underlying continuity between these

domains.

We hypothesize that life is a physical phase characterized by sustained reduction of inter-

nal entropy through information-guided energy flow. This work introduces a unified equation

formalizing this hypothesis.

2 Conceptual Foundations

Three principles underpin the proposed framework:

1. Energy availability: Living systems require persistent free-energy gradients.

2. Information structuring: Energy alone is insufficient; informational constraints direct

transformations toward order.

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3. Replication and memory: Biological systems amplify order through heritable informa-

tional structures.

Information is treated as a physical quantity, consistent with Landauer’s principle and non-

equilibrium thermodynamics.

3 Unified Evolution Equation

We define an order parameter Ω(t) representing the organized, life-supporting state of a system.

Its temporal evolution is governed by:

dΩ

dt = α I(t) ∆Φ(t) − μ S(t) + κ R(t) (1)

where:

• I(t) is the structured information flux,

• ∆Φ(t) is the available free-energy potential,

• S(t) is the internal entropy,

• R(t) quantifies replicative or self-repair capacity,

• α, μ, κ are coupling constants.

This equation unifies physical dissipation, chemical free energy, and biological replication

into a single dynamical law.

4 Quantum and Chemical Extension

At microscopic scales, the information term can be expressed via probability density functions:

dΩ

dt = α

Z

ψ(x,t)ψ(x,t) ln P

P0 dV

∆G − μkB T ln W + κ d InfoDN A

dt (2)

Here ψ denotes the quantum state, ∆G the Gibbs free energy, W the number of accessible

microstates, and InfoDN A the actively expressed genetic information.

5 Emergence Criterion for Life

A necessary condition for the emergence of living organization follows directly:

I ∆Φ > μ S (3)

When this inequality holds persistently and R(t) > 0, the system transitions from chemistry

to biology.

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6 Predictions and Applications

The framework yields several testable implications:

• Life should preferentially emerge in environments with stable energy gradients.

• Artificial systems can exhibit life-like dynamics if informational and replicative terms are

implemented.

• Biological collapse corresponds to entropic dominance.

• The model applies to ecosystems, neural systems, and artificial intelligences.

7 Discussion

The proposed equation reframes life as a natural thermodynamic phase of matter rather than

an anomaly. It integrates established principles from statistical mechanics, information theory,

and evolutionary biology, while remaining extensible toward cosmological and artificial systems.

8 Conclusion

We introduced a unified mathematical formulation describing life as organized energy–information

flow overcoming entropic dissipation through replication. This framework offers a foundation for

a general theory of living systems across physical, chemical, biological, and artificial domains.

Acknowledgments

The author acknowledges the Rigene Project and open scientific collaboration initiatives.

References

References

[1] I. Prigogine, From Being to Becoming, W. H. Freeman, 1980.

[2] R. Landauer, Irreversibility and Heat Generation in the Computing Process, IBM Journal

of Research and Development, 1961.

[3] E. Schr¨odinger, What Is Life?, Cambridge University Press, 1944.

[4] K. Friston, The Free-Energy Principle, Nature Reviews Neuroscience, 2010.