Thermodynamic depth

In human thermodynamics, thermodynamic depth is an information-base supposition that the measure or value of the energy conversions that went into a given product, such as a living being, a peacock’s tail, or a classic poem. [1]

History
The term “thermodynamic depth” stems from the 1988 paper “Complexity as Thermodynamic Depth” by American mechanical engineering Seth Lloyd, who is currently a professor at the MIT school of thermodynamics, and his PhD supervisor at Rockefeller University, American physicist Heinz Pagels. [2] In particular, they state “depth”, a universal measure, applicable to all physical systems, “is a measure of the complexity for the macroscopic states of physical system.” Moreover that: [3]

“The form of the measure [of depth] I uniquely fixed by the requirement that it be a continuous, additive function of the processes that can result in a state … applied to a Hamiltonian system, the measure is equal to the difference between the system’s course- and fine-grained entropy, a quantity that we call thermodynamic depth.”

The definition here, to note, seems to be caught up in a mixture of complexity theory, information theory, computer science, as applied to “systems capable of computation”, and thus not a true thermodynamic term as built on the works of German physicist Rudolf Clausius.

Mate selection
Beginning in 1998, and particularly in 2002, with the publication of The Generous Man, Danish science writer Tor Nørretranders picked up on the concept of thermodynamic depth, only applying it to information exchanges between sexual selecting species, such with animals and with human. [4] In particular, in the process of human communication, Nørretranders’ begins by distinguishing between “exformation”, as that information that churns around in the mind of the sender before speaking as well as the information sparked off in the mind of the receiver before the message is sent, in contrast to “information”, that which is said.

In this sense, exformation are the meaningful aspects of something that is said, not present in the words, but referred to. Thus, according to Nørretranders, “by distinguishing between information and exformation we are able to define what’s costly in a costly signal itself is information, of course, which is measured in bits. But costliness was a manifestation of how difficult producing the signal was: how much it cost the organism to build a peacock tail or to write a poem.” In this sense, according to Nørretranders, the back story is the “depth” of the utterance. In Nørretranders’ view:

“[Sexual attractiveness] depth involves, among other things, thermodynamic depth, which covers all the energy conversions that lead to a given product, such as a living being … thermodynamic depth is thus a measure of the cost of producing something or other.”

On this logic, he notes that “this depth is therefore a measure of the costliness of a signal regarded as physiological effort, metabolite resources, or blood sugar consumption.” This means, according to Nørretranders, that the complexity of a physical system is measured by the resources that went into its production, a measurement that can be quantified thermodynamically as depth.

References
1. Nørretranders, Tor. (2006). The Generous Man: How Helping Others is the Sexist Thing You Can Do, (pg. 180) (English translation). Da Capo Press.
2. Pagels, H. and Lloyd, S. (1988). “Complexity as Thermodynamic Depth”, Ann. Phys. 188: pg. 185.
3. Leff, Harvey S. and Rex, Andrew F. (2003). Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing, (excerpt: Lloyd, S. and Pagels, H., ‘Complexity as Thermodynamic Depth’, pg. 408-09). CRC Press.
4. (a) Nørretranders, Tor. (1998). The User Illusion: Cutting Conscious Down to Size, (pgs. 83-94). A. Lane.
(b) Nørretranders, Tor. (2002). Det generøse menneske. En naturhistorie om at umage giver mage (The Generous Man: A Natural History of the Trouble Image Gives). People's Press.

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