What did Lotka really say? A critical reassessment of the “maximum power principle”

doi:10.1016/j.ecolmodel.2011.02.002

Ecological Modelling

Volume 222, Issue 8, 24 April 2011, Pages 1347-1353

https://doi.org/10.1016/j.ecolmodel.2011.02.002 Get rights and content

Abstract

This paper presents a critical discussion of the so-called “maximum power principle”, often quoted in studies about the energy balance of living systems and also known in the emergy literature as “maximum em-power principle”. Several authors consider this principle highly relevant and some even proposed it as a “fourth law of thermodynamics”. A critical analysis of the original source, namely Alfred Lotka's 1921–22 papers, conducted both in an historical perspective (the connection between Lotka's writings and the ongoing debate at his time) and in a more modern context, leads to a more detailed and less biased assessment. It turns out that in spite of Lotka's very anticipatory and incredibly sharp vision of the possible interconnections between the second law of thermodynamics and evolutionism, doubts arise about the general applicability of his “maximum power principle”. From an accurate analysis of his writings, it can be concluded that: (a) Lotka explicitly and consistently addressed the “optimal use” of the flow of exergy (available energy), and therefore the quantity defined as “em-power” is an incorrect interpretation of Lotka's constrained maximum power principle; (b) “Lotka's principle” can be reformulated within Ziegler's “maximum entropy production” or Prigogine “minimum entropy generation” paradigm only under two different respective sets of rather stringent additional conditions which Lotka was probably already aware of but never explicitly stated.

Research highlights

► This paper presents a critical discussion of the so-called “maximum power principle”, formulated by Alfred Lotka in 1921-22 ► A first conclusion is that Lotka thought (and wrote!) in terms of exergy (available energy) and not energy. ► Another conclusion is that Lotka's principle can be reformulated within Ziegler's “Maximum Entropy Production” or Prigogine “Minimum Entropy Generation” paradigm only under different sets of rather stringent additional conditions. ► A modern restatement of Lotka's principle in evolutionistic terms is presented and discussed.

Section snippets

A brief history of the so-called “maximum empower principle”

In 1921 and 1922, the 23-year old Alfred Lotka published two papers (Lotka, 1922a, Lotka, 1922b) in the Proceedings of the National Academy of Science to present his ideas on how the evolution of a far-from-equilibrium thermodynamic system is correlated to its energy-absorption capacity. These papers are considered to mark the beginning of ecological thermodynamics, in that they explicitly state that the likeliness of a living system to survive and successfully evolve is linked to its ability

Relevant thermodynamic definitions

This section provides a list of definitions for some of the thermodynamic quantities used in the paper.

Energy is a prime concept in Thermodynamics. It is defined as the ability of a system to cause change and, more specifically, to perform mechanical work. In living systems, “energy” is never considered as per its “content” but as per its “flowing”: thermal energy (heat) flows from a body to another, and so do chemical energy, mechanical energy, electrical energy, and so on. Energy is measured

Lotka's statements

To begin with, it is important to understand that Lotka was consistently talking of available energy (i.e., exergy): in his footnote n.1 in (Lotka, 1922a) he makes explicit reference to Boltzmann's 1886 paper (Boltzmann, 1886) in which not the energy, but the available energy content of a flux was considered. This is an essential point, and in the remaining of this paper Lotka's postulate shall be referred to as the “maximum exergy rate principle”.

A second important point is the following:

Can Lotka's principle be regarded as “The Fourth Law of Thermodynamics”?

As we have seen, long before emergy analysts elected their re-formulation of Lotka's principle as the perspective fourth law of thermodynamics, Lotka himself had regarded his constrained maximum exergy rate principle as worthy of being added to the three existing thermodynamic laws. On the basis of the critical analysis developed in Section 2 above, is it correct to conclude that besides the assumptions of existence of an a priori tendency towards equilibrium (0th law), the energy conservation

Discussion: Lotka's view in a modern perspective

Three points can be extracted from the analysis presented in this paper, that are here figuratively “posed on the table” for further discussion:

(a) Lotka thought (and wrote!) in terms of exergy (available energy) and not energy. It is somewhat unfortunate that his “principle” has been taken up by emergy – rather than exergy analysts, because the latter would have immediately compared the maximum exergy rate with the minimum exergy destruction paradigm (which was the real matter of debate

Conclusions

This paper was intended to present a critical analysis of the contents and significance of Alfred Lotka's three seminal 1921–1922 papers, and the fact that it ended up being almost a eulogy for Lotka reflects the profound respect that his intuition, his way of argumenting and his rigor demand of the reader. The analysis shows though that, while his reasoning was correct and his argumentations accurate, the very weakness of Lotka's theory seems indeed to be his insistence on the absolute

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View full text

What did Lotka really say? A critical reassessment of the “maximum power principle”

Abstract

Research highlights

Section snippets

A brief history of the so-called “maximum empower principle”

Relevant thermodynamic definitions

Lotka's statements

Can Lotka's principle be regarded as “The Fourth Law of Thermodynamics”?

Discussion: Lotka's view in a modern perspective

Conclusions

Rep. Math. Phys.

Ecol. Model.

J. Theor. Biol.

Physica

Ecol. Model.

Physica A

Phys. Rep.

Math. Comp. Model.

Energy

Entropy Generation Minimization

Emergy measures of carrying capacity to evaluate economic investments

Popul. Environ.

The maximum power principle predicts the outcomes of two-species competition experiments

Oikos

Evolution

The Maximum Em-power Principle

Thermodynamic Theory of Structure, Stability and Fluctuations

Non-equilibrium Thermodynamics – Field theory and variational principles

Thermodynamics: Foundations and Applications

The Mechanism of Life in Relation to Modern Physical Theory

Energy Hierarchy and Transformity in the Universe

Ecol. Model.