● Final cause → End state (final state)
● Purpose → Realization of a thermodynamic potential (free energy; Gibbs energy minimization) (Lotka, 1945)
● Aristotelian teleology → Clausiusian or Gibbsian based chnopsology
● Telos (inner purpose) → Driving force (internal force; internal drive)
● Sense of purpose (Einstein, 1932) (Ѻ) → Sense of activation energy [?]

“Practically since its first definite formulation by Darwin the concept of chance variation and natural selection has dominated the study of evolution, although frequent attempts have been made to replace or modify it. Probably most such attempts are provoked by a vaguely defined awareness of an insufficiency in the natural selection hypothesis, and the recognition of a directive factor in evolutionary processes which persists through successive generations. The latter concept which is commonly known as ‘orthogenesis’, is supported a by considerable amount of evidence (Leo Berg, 1926), but at present is not widely accepted among biologists. The general reason for abandoning or neglecting this concept has been the failure, thus far, to demonstrate the existence of the necessary directing factor outside of the theological doctrine; and one may suspect that fear of leaning too closely to such doctrine has caused most biologists to ‘shy off’ from orthogenesis. It will be the aim of the writer to indicate the actual existence of a directing factor in evolutionary processes, while at the same time avoiding all necessity of invoking theological concepts.”

“The chemical reactions possible would be limited to those taking place with a decrease in free energy, and thus an increase in entropy. Those not acquainted with the terminology of thermodynamics may, for the purpose of this paper, simply regard free energy and entropy as quantities with opposite signs but not as equivalent; free energy represents chemical potential. For a discussion of the principles of chemical thermo­dynamics see Lewis and Randall (1923).”

“In Blum’s ‘Evolution from a Thermodynamic Point of View’ (1935), we perceive in evolution a certain drive [see: driving force], an inherent direction, which is NOT to be identified on the basis here indicated with any teleological end.”

— Roderick Seidenberg (1950), Post-Historic Man (pg. 151)

“Purposefulness, or teleology, does not exist in nonliving nature. It is universal in the living world. It would make no sense to talk of the purpose or adaption of stars, mountains, or the laws of physics.”

— Theodosius Dobzhansky (c.1970), Publication (Ѻ); cited by Peter Corning (2003) in: Nature’s Magic (pg. 172)

A depiction of Alfred Lotka's 1925 "mechanical walking beetle", in which he explains how the receptors (antennas) give feedback to the adjuster of the body, so to keep the beetle from falling off the table, thus being a mechanical way to show how "future", the likelihood of falling off the table, or seeming purposive behavior (teleology) comes into play.

“The depiction in this case is plainly mechanical or geometric. We, as living, conscious organisms, in certain circumstances exhibit a precisely analogous behavior; our action is determined by a picture (psychic in this case) of the future that we seek to avoid or to attain. We are directly conscious of our own volition (whatever its precise physical significance may be.) We hesitate not at all in describing our action as purposive, as directed to and determined by an end, by a final cause. As to the tin beetle, we have dissected him and fully understand his mechanism. We would think it foolish, with our peep behind the scenes, to impute to him volition or purpose; we describe his action as mechanical, as fully determined by an efficient cause.”

— Alfred Lotka (1915), Elements of Physical Biology 27§§: “Mechanistic and Teleological Interpretation of Adjustors” (pgs. 281-85)

“Free energy. Associated with the transformer is a fund of free energy ready to be released by trigger action, that is, by an expenditure of an amount of energy bearing in general no quantitative relation to the energy released, which can thus be far in excess of the energy applied at the ‘trigger’. It can be noted here, only in passing, that the possession of such a fund of free energy is what gives the opportunity for ‘purposive’ action and the exhibition of the phenomenon of ‘will’, that is, action teleologically aimed at future effects.”

— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 181)

“Since the question whether a process is reversible or irreversible depends solely on the nature of the initial state and of the terminal state of the process, but not on the manner in which the process develops, in the case of an irreversible process the terminal state is in a certain sense more important than the initial state—as if, so to speak, nature ‘preferred’ it to the latter. I saw a measure of this ‘preference’ in Clausius' entropy; and I found the meaning of the second law of thermodynamics in the principle that in every natural process the sum of the entropies of all bodies involved in the process increases. I worked out these ideas in my doctoral dissertation at the University of Munich, which was completed in 1879.”

— Max Planck (1949), Scientific Autobiography (pgs. 18)

“The teleological idea or concept of purpose is involved in several physical principles, notably Hamilton’s principle and the related but identical principle of least action, Hertz’s principle of the straightest path, Gauss’ principle of least constraint, and Fermat’s principle of least time. They all effectively state that things take place in the physical world, e.g. the motions of systems of particles, in such a way as to make a certain function assume a stationary value under certain boundary conditions, usually a minimum as compared with all possible values satisfying the given conditions.

This means that the actual motion between the initial state and final states at the initial and final times, respectively, takes place in such a way that the integral in question is either greater than it would be for any other possible motion between these states or less than any other possible motion between these states, it being understood that the initial and final states are the same for all the possible motions being compared. In the majority of cases to which the principle has been applied in classical mechanics, the stationary value is a minimum.

With respect to the possible idea of purpose involved philosophers have argued that since Hamilton’s principle is not necessary for the deduction of the actual motion of the dynamical systems, i.e. the Newtonian or Lagrangian equations are fully adequate, we have no real logical ground for insisting that nature imposes a teleological requirement on motions in our experience. Nevertheless the fact that one can exhibit the principles of mechanics in a teleological guise is persuasive, since it serves to tie physical principles with an idea basic to the interpretation that human beings give too much of their ordinary experience, particularly in their relations with other human beings.

Hamilton’s principle, e.g., says that for a conservative dynamical system the motion between any two instants of time is such that the time integral of the difference between the kinetic and potential energies taken between these two instances has a stationary value. It has as if the system had a certain purpose to satisfy. A rational individual is said to arrange his actions so as to be sure of achieving his fundamental desires, whether it be to accumulate wealth or gain power over his fellow men. In particular, the aim here is almost always to try to attain the given desired end at minimum cost in human effort. This strongly suggests a heuristic connection with the [Gibbsian] minimum principles of physics.”

A visual of the so-called “Gates model”, from the 2015 “Zerotheism for Kids: Lecture 4: Enthalpy & Entropy, Moral Compass, and Monism” (Ѻ) (14:47-) video, by Libb Thims, also discussed in the 2014 “25 Smartest People Alive | Existive (2 of 5) (Ѻ) (3:49-8:40) video, therein depicting a visual of the “gravito-electromagnetic force”, aka Gibbs force (see: force function), that moved Bill Gates, from his two person initial state, through his reaction coordinates, over the activation energy barrier, forming the activated complex of the 11-member Microsoft “group” at the apex, and “falling” into the product stage (end state) of the Microsoft corporation, valued at $341 billion in 2015, employing some 120 thousand people, which is akin to the “gravitational force” causing a rock to fall through its gravitational potential, say if tipped off a cliff.

“Re (#4): “where is the director?” [Kierkegaard], this brings to mind the so-called purpose question—which you commented somewhere, in some thread, was your point or apex of debate collision with me—and what Bruce Lindsay (1983) has to say about this in regards to physics, the teleology debate issue, and sense of purpose. The key statement being the following:

‘A rational individual is said to arrange his actions so as to be sure of achieving his fundamental desires, whether it be to accumulate wealth or gain power over his fellow men. In particular the aim here is almost always to try to attain the given desired end at minimum cost in human effort. This strongly suggests a heuristic connection with the minimum principles of physics.’

Prior to this, Lindsay cites the following so-called minimum principles: Newtonian (not exactly a minimum principle) → Lagrangian → Hamiltonian, and how they have merged into each other, to increasingly quantify the dynamics of the motions of systems comprised of moving particles (e.g. social systems). What he doesn’t state, however, is that the Hamiltonian, via Clausius (1865) and Gibbs (1876), got transformed into the so-called ‘Gibbsian’ minimum principle, according to which Lindsay’s statement, in 2014 retrospect, is something along the lines of:

‘A rational individual is said to arrange his actions so as to be sure of achieving his fundamental desires, whether it be to accumulate wealth or gain power … the aim here is almost always to try to attain the given desired end at minimum cost in human effort. This strongly suggests a heuristic connection with the [Gibbsian] minimum principles of the [physicochemical sciences].’

And hence, if as a rational individual, as Lindsay says, you desire to understand your desires, you are led naturally enough into a study of the so-called ‘human free energy’ theorists, so as to better understand the ‘whys’ and ‘hows’ associate with ‘minimum principles’ as they related to the arrangements your actions. This is not to say, to note, that atoms, molecules, and concordantly humans have "purpose", so to say, in the sense of ‘the purpose of hydrogen is to bond with oxygen to form water’, etc., as this is a type of non-sensical statement, whereby so it must also be so with humans (or human molecules), or are governed by "teleological" principles, as the covert religion-siding scientists like to argue, as this is an model that only works in an Aristotelian universe, but rather that there seems to be some well-honed truth, in need of deeper clarification, in what Lindsay states above.”