Self-Organization as the Ultimate Variational Principle of Nature
Sungchul Ji, Ph.D.
Emeritus Professor of Theoretical Cell Biology
Ernest Mario School of Pharmacy, Rutgers University
October 16, 2025
1. The Hidden Logic of Nature
From the motion of planets to the folding of proteins and the metabolism of cells, nature seems to follow a universal logic of efficiency and harmony.
Physicists call it the variational principle—the idea that every system evolves along a path that optimizes some quantity of significance: energy, entropy, or information.
I propose that this principle culminates in self-organization itself—the process by which energy and information co-operate to generate stable yet adaptive forms. In this view, life is not an exception to physics but its highest expression: the variational principle of the universe made manifest.
2. Classical Variational Principles: The Economy of Motion
In the 18th century, Maupertuis, Lagrange, and Hamilton discovered that all of mechanics could be derived from one deceptively simple equation:
Here, is the Lagrangian, the difference between kinetic and potential energy.
This Principle of Least Action tells us that nature chooses the trajectory for which the action is stationary—unchanged to first order.
From this equation flow the Euler–Lagrange equations governing particles, waves, and fields alike. It expresses the economy of nature: everything happens in the most harmonious way possible given the constraints.
3. Thermodynamics: The Variational Logic of Entropy
The same logic reappears in thermodynamics, where the key quantity is entropy. An isolated system evolves toward maximum entropy—the most probable macrostate consistent with its constraints.
For open systems, Ilya Prigogine and Lars Onsager showed that steady states obey a complementary rule:
They called this the Principle of Minimum Entropy Production.
Thus, equilibrium (maximum entropy) and non-equilibrium (minimum entropy production) are two sides of the same variational coin. Nature always finds balance by extremizing a quantity that encodes efficiency.
4. Living Systems: The Rise of Self-Organization
Living organisms are open, far-from-equilibrium systems that continuously exchange energy, matter, and information with their environments. They maintain low internal entropy by exporting disorder outward—creating order through flow.
Prigogine called such entities dissipative structures [3]: systems that persist through dynamic exchange rather than static equilibrium.
But what do living systems optimize?
Not merely energy or entropy—but organization itself, in order to maintain structure and self-reproduction.
In this sense, life is the variational optimization of organization—the emergence of purpose through thermodynamic flow.
5. The Gnergy Principle of Organization (GPO)
In The Cell Language Theory [1], I proposed that all organization—physical, biological, or mental—requires the integration of:
Energy (E): to perform work
Information (I): to control that work
These two orthogonal quantities combine into a single complex term called gnergy:
where (the imaginary unit) symbolizes the orthogonal relationship between energy and information.
From this arises the Gnergy Principle of Organization (GPO):
This generalizes the variational principle to open systems:
As complexity increases, the optimized quantity becomes richer—expanding from energy to entropy, and finally to gnergy, the complex unity of both.
6. Self-Organization as Nature’s Ultimate Optimization
Self-organization emerges when energy flow and information flow reach dynamic equilibrium within an self-organizing environmental context. At this point, systems achieve a metastable optimum—stable enough to persist, flexible enough to adapt.
A crystal has perfect order but no freedom.
A gas has freedom but no structure.
A living cell balances both through gnergic coordination.
Hence, self-organization represents the ultimate variational principle:
Nature doesn’t merely minimize or maximize—it self-optimizes by maintaining the delicate balance between constraint and possibility to accomplish self-organization.
In triadic terms:
X (Energy) – drives change
Y (Information) – guides change
Z (Environment / Meaning) – selects what persists and self-reproduce
Together they form the Gnergiton, the triadic unit of reality that underlies every act of organization.
7. From Lagrangian to Gnergy: Extending the Variational Principle to Life
Physicist and systems theorist Paul Werbos [4] has long emphasized the power of the Lagrangian and entropy functions as windows into ultimate reality—including life and consciousness. In his writings on intelligent control, neural networks, and cosmology, Werbos proposes that the universe itself may operate as a Lagrangian optimization process, minimizing a generalized “cost” function that blends energy and information.
This insight is profound, yet it highlights a crucial distinction:the classical Lagrangian formalism applies to isolated, conservative systems, whereas life and mind are open, dissipative systems. In a Lagrangian framework, total energy is conserved and time is reversible:
Living systems, however, depend on continuous exchange of energy, matter, and information with their surroundings. They thrive through entropy export, information inflow, and irreversibility—all absent from the closed-system Lagrangian picture.
Werbos’s approach can therefore be seen as an ontological extension of the Lagrangian paradigm into the open-system realm.
My own framework formalizes that extension through the Gnergy Principle of Organization (GPO) [1, 2]:
Here drives work, controls work, and expresses their orthogonality.
This transforms the variational logic from mechanical efficiency to organizational creativity.
In this light, Werbos’s generalized Lagrangian and the Gnergy Principle are complementary formulations of nature’s deeper logic.
Both seek a unifying variational description of existence, but Gnergy explicitly includes the informational and environmental dimensions necessary to describe life, mind, and evolution as open systems.
8. Toward a Unified Science of Organization
From Lagrange’s equations to living metabolism, the same logic echoes across all scales:
Nature evolves by extremizing integrated quantities of constraint and possibility.
The Principle of Least Action was the beginning.
The Principle of Maximum Entropy extended it.
The Gnergy and Gnergiton Principles [1, 2]—and the Self-Organization Principle it embodies—may be the next great unifier, showing that life is not accidental but the natural outcome of the universe’s drive to organize itself [5, 6].
9. Conclusion
The cosmos doesn’t merely exist—it organizes itself.
The atom, the cell, and the mind are all local expressions of one universal variational law:
where energy and information coevolve under environmental selection (guided by Spirit/Consciousness), weaving the visible and invisible aspects of reality into one living tapestry.
In this sense, self-organization is the ultimate variational principle of Nature—the law through which the universe learns to become itself.
References
Ji, S. (2018). The Cell Language Theory: Connecting Mind and Matter. World Scientific.
2. Ji, S. (2025). The Geometry of Reality (GOR): A Triadic Framework for Matter, Mind, and Spirit. https://622622.substack.com/p/geometry-of-reality
3. Ji, S. (2012). Principle of Self-Organization and Dissipative Structures. In: Molecular Theory of the Living Cell. Springer, New York. pp. 69–84.
4. Werbos, P. (2025).https://drive.google.com/drive/folders/1q-7LVt6cyCAZtUZ8slMFELjWnHXwMzge?usp=sharing
5. Ji, S. (2012). Op. cit. Pp. 460-463.
6. Ji, S. (20250. Three Kinds of Order in the Universe. https://622622.substack.com/p/three-kinds-of-order-in-the-universe