A good starting point would be to learn classical thermodynamics. Then you should see that the thermodynamic entropy has nothing to do with your questions.

Thank you for your reply. I appreciate the reminder to be precise in how thermodynamic terms are used—especially when bridging across disciplines.

To clarify my original question, I recognize that in classical thermodynamics, entropy is a rigorously defined statistical measure tied to microstate multiplicity. However, in non-equilibrium and open-system contexts, especially in biological and cognitive systems, there have been proposals (e.g., Swenson’s "Fourth Law") that suggest spontaneous ordering may correlate with increased entropy production, particularly under conditions where boundary constraints and energy flow enable structure formation.

In light of that, I’d like to reframe my inquiry more precisely:

Are there critiques, alternatives, or formalisms within nonequilibrium thermodynamics, systems biology, or complexity science that seriously engage with Swenson’s fourth law, or similar proposition, that tie entropy production to the emergence of order or function in far-from-equilibrium systems?

I’m asking this as someone working within an exploratory theoretical framework (ODTBT) that models structure formation through recursive oscillatory coherence. My intuition draws from systems theory and quantum thermodynamics, but I acknowledge there are likely terminological and formal gaps between what I’m intuitively grasping and how it’s typically articulated in more rigorous thermodynamic language.

If you or others have suggestions for readings, frameworks, or critiques in this space, I’d sincerely welcome the opportunity to learn more.

Warm regards

No, I have meant classical thermodynamics. Search for JANAF (Joint Army Navy Air Force) Thermochemical Tables, they are available online. In each table for a substance there is a column with entropy values. This is the very first level to understand entropy - how it is determined from experimental values. On top of this there is the Clausius inequality that leads to computational method to compute equilibrium composition. The military name means that it got to be used to estimate rocket propulsion.

The next step is to check transport equation in continuum mechanics. This leads us to irreversible thermodynamics where entropy production is introduced. Say, Prigogine's Nobel Prize - dissipative processes, order from chaos, etc. But things get involved and there are more words at this level than equations with which one can really compute something. Well, some special cases are indeed worked out but they are quite far away from your requirements.

On top of this there is so called principle of maximum entropy production. Yet, things are much worse here as one can state the principle but it is actually almost impossible to apply it to solve a concrete problem.

I have once browsed Swenson's work. I am sorry but it is just qualitative considerations. Hence its relationship with thermodynamics is already broken. Thermodynamics used to allow us to solve real problems - see JANAF and computation of equilibria. Swenson's work on the other side is pure natural philosophy that cannot be applied to real problems.

Thank you again for your thoughtful and technically grounded response. Your outline of the modeling tiers, from empirically derived entropy values in the JANAF tables to Clausius-based equilibrium computations and continuum transport equations, was especially helpful in clarifying the computational foundations of classical thermodynamics.

I agree fully that these tools are essential, especially in high-precision applications like propulsion modeling and chemical equilibrium calculations, and I plan to spend more time reviewing those systems in depth.

That said, part of my motivation stems from a desire to explore whether conceptual models, like Swenson’s work and my own development of the Oscillatory Dynamics Transductive-Bridging Theorem (ODTBT), might eventually contribute to a deeper field-based understanding of how coherence and order emerge in open, nonequilibrium, and biologically active systems.

I'm not aiming to replace thermodynamic computation, but to examine its ontological scaffolding, particularly in relation to recursive structure, phase dynamics, and information-based coherence.

To that end, I’ve recently completed a short primer titled:

Surmont, J. (2025). From Entropy to Coherence: A Transductive Reframing of Thermodynamic Structure through ODTBT. ResearchGate Preprint. https://doi.org/10.13140/RG.2.2.28668.24965

This is not an attempt to substitute metaphor for rigor, but to explore whether entropy production, negentropic gain, and phase transitions may reflect deeper TWIST-regulated oscillatory dynamics across nested holonic systems.

I’d welcome any critique or further reading suggestions you may have. Thank you again for engaging this conversation so constructively.

John Surmont,

This is not directly related to Swensen's argument, but it might be of interest to you in your study of biological systems.

I recently made a study on the latest research into enzymes and the role they play in cells and organisms. I was surprised to see that enzymes clearly decrease the entropy in the chemical reactions that they catalyze. There is no question about this. Increasing the order between the substrates is how they accelerate chemical reactions.

If you add this interesting fact to the second fact that enzymes are actively involved in over 99% of all the chemical reactions that take place in cells, then it is easy to see how organisms sustain themselves in a state far from equilibrium with the environment.

Perhaps this might be relevant to what you are working on.