Mr. Nathan has rightly mentioned that work (energy) can be turned into an equivalent amount of information. Information can be turned into an equivalent amount of work (energy). Since high energy efficiency is required in a sensor network, it is desirable to disseminate query messages with small traffic overhead and to collect sensing data with low energy consumption. But the question before us is about energy-cost of information retreival .

In informatics, instead of speaking of energy the unit step is is used. How many steps does it take to retrieve an information? What one step actually in seconds means depends on your hardware. You can always buy a faster computer, so constant factors play no role. The computational complexity is denoted in O-notation:

https://en.wikipedia.org/wiki/Big_O_notation

For example, if an operation needs k steps depending on the input size, its complexity is O(k). If it takes 2k steps, its complexity is also O(k), see

https://en.wikipedia.org/wiki/Big_O_notation#Multiplication_by_a_constant

If you retrieve data through a channel, usually a short message is sent: "Give me records 443 to 449". The answer can be lengthy and depends on the size of the data to return (e.g. images, mp3 files?).

The complexity of retrieval does also depend on the data structure in which the information is stored. For example, if you search in a lexicon for a word, you can apply binary search. You won't go through every word sequentially. So the complexity of searching a word in an ordered list of length n is O(log(n)).

A faster data structure is the hash table, also called associative array. Records are stored at places that can be computed by a key value contained in the record. In the best case, if you want to retrieve a record by its key, you compute the place where the record should be, get it and return it. Occasionally some (a few) records are mapped to the same location. This is handled for example with smaller lists. Thus the complexity of retrieving one record from a hash table is about O(1), maybe a little bit bigger, because of this collision handling.

For human memory recall you can also assume an O(1) operation. To be more precise: you use one or more symbols as a key, do the remembering and get a resulting symbol tuple which is then stored into working memory.

The complexity is of course bigger if you have to go through many memories. An example: how many friends do you have whose surname has 'r' as the third letter? In this case you have to recall all of your friends systematically into working memory and have to test each one. A detailed analysis must always be done, but constant factors play no role.

Regards,

Joachim

I'm going to rephrase your question if that's ok, as I believe "query-and-retrieval" may allude to additional steps.

"If energy cost of the transmission (sending) information is 1, should the act of receiving this same information be 2? Assume all other variables such as channel, noise, etc. are absolutely controlled."

But to answer your question:

No. "It would also be 1."

I wanted to say that, but that's not true. Your answer is at the bottom.

Why? If someone is reading this, they should drink some coffee.

See references and associated formulas within below (formulas attached, I'm not going to copy and paste them into here..and all references have formulas within them).

De la Cruz, J., and M. Martin-Delgado (2016), Enhanced Energy Distribution for Quantum Information Heat Engines, Entropy, 18(9), 335, doi:10.3390/e18090335.

"In order to find a relation between the two possible uses of messenger systems, a mutual limitation between communication and energy has been derived in Section 4 leading to Equation (20). This result seems quite natural, from the complementary perspectives of gaining certainty (communication) and increasing uncertainty (traded for work)."

Ok, author proposes/derives a mutual limitation between

communication work (use of energy)

communication (transfer of information) energy

Brandão, Fernando, Michał Horodecki, Nelly Ng, Jonathan Oppenheim, and Stephanie Wehner. 2015. The second laws of quantum thermodynamics. Proceedings of the National Academy of Sciences 112 (11): 3275–3279.

"What is interesting about this comparison is that while in our model, work is stored in the form of energy, in [13, 34] the work is quantifed by means of purity, i.e. how many pure qubits we invest/create during the process of state transformation. The significance of information to work extraction has been discussed by various works [13, 42, 43]. In particular, Landauer’s principle [15, 44] states that any physical process that erases one bit of information (i.e., creating purity) in an environment of temperature T has a fundamental average work cost of kT ln(2). Similarly, by ulitizing one bit of information stored (i.e., consuming purity) in a physical system, and allowing it to interact with a thermal bath at temperature T , one can draw an average work of kT ln(2)."

Ok, so they relate information-work(use of energy) to "purity".

If you use "purity" (utilize info/increase uncertainty) you get work.

If you create "purity" (erase info, ie pin it down to what it is) you lose work.

1 bit = kTln(2) of work

kTln(2) of work = 1 bit

kTln(2) of work 1 bit

Use information --> work(gain energy)

Work(use of energy) --> information

energy information

Work (Energy) can be turned into an equivalent amount of information.

Information can be turned into an equivalent amount of work (Energy).

Makes sense intuitively though, doesn't it?

In essence it's like they are different forms of the same thing. Hmmm.

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Janssens, and Maassen. 2006 Information transfer implies state collapse. Journal of Physics A: Mathematical and General 39(31): 9845. doi:10.1088/0305-4470/39/31/01

"We attempt to clarify certain puzzles concerning state collapse. In open quantum systems decoherence is a necessary consequence of the transfer of information to the outside; we prove an upper bound for the amount of coherence which can survive such a transfer."

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Decoherence is when the entanglement of a quantum system spreads out to the environment, and a quantum system is one that is entangled in some way.

Entanglement is lost by the action of decoherence (spreading/averaging out of that initial entanglement to the environment).

So, information transfer --> decoherence.

Is there really a "transfer" of information though...ever...?

You can call it that, but it's really more just "information" in my opinion. But, really "information" probably means the "localization" of "information". Any use of the word "lost" information just means it went into the environment....just like energy cannot be created or destroyed. I'm just going to say "information."

information decoherence (although it is not measured here, Brandão, Fernando have a thorough paper on all this)

Hmmm...ok

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Auletta,G. (2014) Entanglement, Information, Causality. Epj Web Conf, 70, 00001.

"The most general conclusion is that information can be defined as correlation among possible out- comes or events, as we have seen above for the mutual–information expression of entanglement."

Ok, a -mutual- information expression of entanglement.

information entanglement

but if

information decoherence

and decoherence is the loss of entanglement

we can say

information dynamics dynamics of entanglement/decoherence

Time and entanglement dynamics are, in my opinion, integrally related. But that's too crazy for some people.

Jha, A., Malik, M., and Boyd, R. (2008). Exploring energy-time entanglement using geometric phase. Phys Rev Lett 101, 180405.

"We thus show that energy-time entanglement between the signal and idler photons can be explored by means of their geometric phases. These results may have important practical implications for quantum information science by providing an additional means by which entanglement can be manipulated. "

Just the use of the phrase "energy-time entanglement".

Shalm, L., D. Hamel, Z. Yan, C. Simon, K. Resch and T. Jennewein, ‘Three-photon energy–time entanglement’ in Nature Physics, ix, no. 1 (2012), p. nphys2492

"States of the form in equation (1) can violate all the inequalities maximally, namely the left-hand side goes to zero, and thus exhibit genuine tripartite entanglement."

"Our three photons strongly violate inequalities (9)–(12) and are genuinely tripartite entangled. The state exhibits energy–time correlations close to the ideal state described in equation (1) where the time–bandwidth products are exactly zero. This state is the continuous-variable analogue to the famous Greenberger, Horne and Zeilinger entangled state18,24, and the natural extension of the two-party continuous-variable Einstein–Podolsky–Rosen state 15,16,25 "

You'll see alot of research saying how the there's an inequality in that in essence "information" is lost whenever it is well, transferred. Well, maybe you lost the information and the environment has the information now?

Interesting, the inequalities are violated when there is more than one within the ensemble of entanglements. I didn't know that, kind of weird, but I'd have to look at the work more.

Anyways, now we have energy-time correlations close to the ideal state.

energy time ?

energy time

notice there's some entanglement in there too

Fiscaletti, D. & Sorli, A. (2017). Searching for an adequate relation between time and entanglement.Quantum Studies: Mathematics and Foundations. 4 (4). p.pp. 357–374.

"This model of space and time embraces elementary particles and stellar objects, all moving in space only, and time being duration of their motion in

the three-dimensional space, originating from the quantum vacuum, which is the immediate medium of quantum entanglement."

Time being the duration of their motion in 3d space, from the QV, which is the immediate medium of quantum entanglement.

From this one I'm going to say

time entanglement

but then also

time decoherence too

so

time dynamics of entanglement & decoherence

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Ok so here's my collection and then conclusion. I'm basing this off of my interpretation of citations collectively.

energy information

information decoherence

information entanglement

information dynamics dynamics of entanglement/decoherence

energy time

time dynamics of entanglement & decoherence

In fact, these are all perfectly proportional universally. The medium does matter though, and should be factored in somehow. I'll explain why if someone asks. I'm not going to introduce consciousness here.

energy information decoherence/entanglement time

I think this is kind of obvious seeing as IBM has already made a quantum computer but that it only lasts for a VERY short period of time and likely requires a tremendous amount of energy.

-------------------------------

The energy cost is the transfer of information be it storing or retrieval.

The energy converts to information which converts to energy.

Some may be lost due to decoherence.

Just like energy can take on many different forms, there is something else that supersedes it and can also take on many different forms too, and I don't think there's a name for it yet.

Thank you, Joachim!

Yes, of course in computer science the number of steps is the complexity measure, yes, yes... The big Os small os etc asymptotic notations and hash tables are something I am well aware of (let's hope.. I give lectures in this).

I think the important hint you give is here: " In this case you have to recall all of your friends systematically into working memory and have to test each one. " Becouse in the model one of the branches (channels of information transmission) causes a working memory charge. The Theorem that I apply requires to assighn different weights to the branches of a binary tree. I have charged the right brancges whith a cost of 2 becouse they use WM, but have to think more and to explain it better. Intuitively, the WM charge can be presented as a Select From Where, in all cases this was my initial idea. I am glad you say something of quite similar.

The final complexity estimation of the calculus is in number of operations, clearly.

Regards!

Thank you, Nathan!

You perephrased my question as: "If energy cost of the transmission (sending) information is 1, should the act of receiving this same information be 2? " .

Well, I would answer "No, it would be 1!". As you did. And...

And you said at the end " The energy cost is the transfer of information be it storing or retrieval. "

The reasoning you provide concerning energy information is a very cofee-drink making one. I took some coffees. After the coffees, I reasoned that, in some philosophical sense, energy and information can be properly defined unically within a concrete domain as they have axiomatic nature.

I have taken a look before at the quantum second low of TD. I intuitively agree that energy and information are somehow the same. To be honest, when time appeared in the reasoning I got lost. One may also include matter in the play, as matter can be seen as energy in traps. So one may measure his/her kgs with jouls. And this wll be true in a very practical sense of a diet. (Perhaps I took more coffees than I should.)

To show you my simple model-resoning, imagine a telephone line (as in the initial Shannon noisy channel) and codes. We are not interresetd in the capacity of the channel or in the codding. To get these codes tramsmitted, we need Energy. To respect mertics , we have the rule "E(from a to b) equals E(from b to a)".

I have difficulties to imagine how the energy needed to tranfer n codes from a to b (or in the opsit sense) will be equal to the information that the codes bring.

Should I take more coffee?

Sincerely

Velina,

We just became more entangled than we were right before you read this, and that was already pretty entangled. Indeed, coffee can have that effect, or the perception of it :)

So let me ask you,

https://www.youtube.com/watch?v=5l-PjIqPOBw ?

I will gladly answer your question or at least have fun trying Velina, ha..and I may try anyway..., despite the fact that your background doesn't at all mean you already know the answer. :)

The thing is I'm just thinking..."how deep did she just go? Ah, Very Deep." Best answer ever btw. I wonder if anyone else will catch it.

Hi Nathan,

Thank you! Yea, for now it is more than enough that you captured it. Well, if I had the answer I would not ask the question.

The more entangled - Velina

Could you define "unidirectional" in your context?

From a to b. Bottom-up, in cognitive terms of flow-reasonning. The query-and-retrieval is done Top-Down, in these same terms.

Mr. Nathan has rightly mentioned that work (energy) can be turned into an equivalent amount of information. Information can be turned into an equivalent amount of work (energy). Since high energy efficiency is required in a sensor network, it is desirable to disseminate query messages with small traffic overhead and to collect sensing data with low energy consumption. But the question before us is about energy-cost of information retreival .

Thank you, Suresh!

Your reasoning and proposal are wonderful, in the context of construction. The problem is that I do not construct whatever. The brain is already constructed, I try to understand what happens using models. The main assimption is that the brain has been constructed with respect of the principle of maximum work performed with minimum energy. One has to define the work it performs and the energy per unit of it. Something like that.

Often Zipf's law is cited when it comes to efficiency of words.

https://www.eurekalert.org/pub_releases/2009-07/f-sf-hla073009.php

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3048148/

https://www.eurekalert.org/pub_releases/2011-09/lsoa-lsv083111.php

https://www.researchgate.net/publication/235971274_A_cross-Language_Perspective_on_Speech_Information_Rate

Regards,

Joachim