Circuits, Symmetry, and Category Theory: A Fresh Look at the Memristor

Image generated by ChatGPT.

As it sometime happens to me while I was checking what’s new on YouTube the suggestions algorithm had a video about Memristor which was a forth basic electrical element that had a memory in it. While I was watching that interesting video that was created by prof. Giordano Scarciotti I saw the symmetry diagram that prof. Leon Chua came up with back in 1971. In that paper he proposed Memristor as a missing fundamental component in electrical circuit theory. So, what’s interesting about that diagram that it very much resembles diagrams in Category Theory.

Introduction

  • Resistor: relates voltage V and current i.
  • Capacitor: relates voltage V and charge q.
  • Inductor: relates current i and magnetic flux φ.

But in 1971, Leon Chua predicted a missing fourth element — the memristor — which connects charge q and flux φ. This completed the symmetry among the four fundamental electrical quantities.

🔎 Constitutive Relations and the “=0” Notation

In advanced circuit theory, each element is defined by a constitutive relation: a constraint between two variables. Instead of writing explicit formulas like Ohm’s Law (V = R·i), theorists often use an implicit form:

  • Resistor: R(V, i) = 0
  • Capacitor: C(V, q) = 0
  • Inductor: L(i, φ) = 0
  • Memristor: M(q, φ) = 0

This doesn’t mean resistance is zero. It means: the pair of variables must satisfy some relation enforced by the element. For a linear resistor, that relation is V − R·i = 0. For nonlinear devices, the relation could be more complex. The implicit form is powerful because it generalizes to nonlinear, time-varying, and memory-dependent behaviors.

🔄 Symmetry and Completeness

Chua’s insight was that with four fundamental quantities (V, i, q, φ), there should be six possible pairings. Three were already realized by resistor, capacitor, and inductor. The missing link — charge to flux — was filled by the memristor. This symmetry is what makes the framework elegant: every pair of quantities is connected by a constitutive relation.

🧩 A Category-Theoretic Perspective

Here’s where the categorical flavor comes in. The symmetry looks a lot like category theory:

  • Objects: The four quantities (V, i, q, φ).
  • Morphisms: The four elements (resistor, capacitor, inductor, memristor).
  • Composition: Just as morphisms compose in category theory, circuit elements combine to form networks.
  • Commutativity: The square diagram commutes:
    L ∘ R = M ∘ C
    meaning that whether voltage is mapped to flux via current (resistor → inductor) or via charge (capacitor → memristor), the structural mapping is consistent.

🖼️ ASCII Diagrams

Fundamental Square of Relations

   V ──R──▶ i
   │        │
   C        L
   │        │
   ▼        ▼
   q ──M──▶ φ
  • R : V → i (Resistor)
  • C : V → q (Capacitor)
  • L : i → φ (Inductor)
  • M : q → φ (Memristor)

Commutative Diagram

        V
       / \
      R   C
     /     \
    i       q
     \     /
      L   M
       \ /
        φ

Here, the two paths from V to φ are equivalent:
L ∘ R = M ∘ C

✨ Why This Matters

Thinking categorically opens new doors:

  • Circuits can be modeled as categories of physical quantities.
  • Functorial translations could connect circuit categories to computational categories (logic, automata).
  • Neuromorphic computing, where memristors play a central role, might benefit from categorical semantics.

The memristor isn’t just a missing device — it’s the morphism that makes the diagram commute, completing the symmetry both physically and mathematically.

🧠 The Main Idea

By reframing Chua’s symmetry in categorical terms, we see circuits not just as physical devices but as mathematical structures. The memristor completes not only the physics of passive elements but also the mathematics of a commutative square.

Understand any programing language using chatbots

Generated by Windows Copilot

Using chatbots wisely

Original post

I suppose there’s a whole class of programmers for whom a compiler is akin to magic, but knowing what’s getting emitted and how it works is fundamental to your success over the long haul. Write some assembly. Read the Dragon book on an airplane. AI will still be here when you get back. In five years, anyone capable of structured thought will be able to become a prompt engineer, but only 1% of software developers will actually be able to debug the stuff that comes out the other end. Be the 1%

What did I do next?

Here’s the full transcription of the PDP-11 assembly code using MACRO-11 syntax, followed by a detailed explanation:
Transcribed Code

.TITLE  BTOA                ; Program title
.MCALL  .PRINT,.EXIT,.TTYOUT ; System macros

HELLOMSG: .ASCIZ /BTOA Example/

        .EVEN               ; Ensure we're on a word boundary

START:  .PRINT  #HELLOMSG
        MOV     #12345., R0 ; Number to convert
        JSR     PC, BTOA
        .EXIT

BTOA:
        MOV     R0, -(SP)   ; Save R0 on stack
        MOV     R1, -(SP)   ; Save R1 on stack
        MOV     R2, -(SP)   ; Save R2 on stack

        MOV     R0, R1      ; Move number to R1 (low part of dividend)
        CLR     R0          ; Clear R0 (high part of dividend)
        DIV     #10., R0    ; Divide R0:R1 by 10, quotient in R0, remainder in R1

        TST     R0          ; Check if quotient is 0
        BEQ     PRINT       ; If quotient is 0, print digit
        JSR     PC, BTOA    ; Recursive call with quotient

PRINT:  ADD     #'0, R1     ; Convert remainder to ASCII
        MOV     R1, R0      ; Move ASCII digit to R0
        .TTYOUT R0          ; Print the digit

        MOV     (SP)+, R2   ; Restore R2
        MOV     (SP)+, R1   ; Restore R1
        MOV     (SP)+, R0   ; Restore R0
        RTS     PC          ; Return

.END    START

🧠 Explanation

This program converts a binary number (in this case, 12345) to its ASCII decimal representation and prints it to the terminal.

🔹 Header and Setup

  • .TITLE BTOA: Sets the title of the program.
  • .MCALL .PRINT,.EXIT,.TTYOUT: Declares macros for printing, exiting, and terminal output.
  • HELLOMSG: .ASCIZ /BTOA Example/: Defines a null-terminated string.
  • .EVEN: Ensures the next instruction is aligned on a word boundary.

🔹 Main Routine (START)

  • .PRINT #HELLOMSG: Prints the greeting message.
  • MOV #12345., R0: Loads the number 12345 into register R0.
  • JSR PC, BTOA: Calls the BTOA subroutine to convert and print the number.
  • .EXIT: Ends the program.

🔹 Subroutine (BTOA)

  • Saves registers R0, R1, and R2 to the stack.
  • Sets up for division: moves the number to R1, clears R0 to form a 32-bit dividend.
  • DIV #10., R0: Divides R0:R1 by 10. Quotient goes to R0, remainder to R1.
  • TST R0: Tests if quotient is zero.
    • If yes, go to PRINT.
    • If not, recursively call BTOA with the quotient.
  • PRINT: Converts the remainder (digit) to ASCII by adding '0', then outputs it using .TTYOUT.
  • Restores registers from the stack and returns.

This recursive approach ensures digits are printed in the correct order (most significant to least significant). Would you like to see how this would look in C or another language for comparison?


Great question! 🧠

BTOA stands for Binary To ASCII. It’s a common abbreviation used in programming to describe the process of converting a binary (or numeric) value into its ASCII character representation, typically for display or output purposes.

🔍 What does “Binary to ASCII” mean?

  • Binary: In this context, it refers to a numeric value stored in binary format (e.g., the number 12345 in machine-readable form).
  • ASCII: The American Standard Code for Information Interchange — a character encoding standard that maps numbers to printable characters like '0' to '9', 'A' to 'Z', etc.

        MOV     R0, R1      ; Move number to R1 (low part of dividend)
        CLR     R0          ; Clear R0 (high part of dividend)
        DIV     #10., R0    ; Divide R0:R1 by 10, quotient in R0, remainder in R1

        TST     R0          ; Check if quotient is 0
        BEQ     PRINT       ; If quotient is 0, print digit
        JSR     PC, BTOA    ; Recursive call with quotient

This block of PDP-11 assembly code is the core of the binary-to-ASCII conversion logic. It performs division by 10 to extract digits from a number and uses recursion to print them in the correct order. Here’s a breakdown of each line:

🔍 Line-by-Line Explanation

18 MOV R0, R1 ; Move number to R1 (low part of dividend)
  • Copies the number from R0 to R1.
  • This sets up the 32-bit dividend for division: R0:R1 (high:low).
19 CLR R0 ; Clear R0 (high part of dividend)
  • Clears R0 to zero.
  • Now the full dividend is 0:R1, effectively treating the original number as a 32-bit value with high word = 0.
20 DIV #10., R0 ; Divide R0:R1 by 10, quotient in R0, remainder in R1
  • Performs a 32-bit division of R0:R1 by 10.
  • After this:
  • R0 contains the quotient (i.e., number / 10)
  • R1 contains the remainder (i.e., number % 10), which is the rightmost digit
22 TST R0 ; Check if quotient is 0
  • Tests if the quotient is zero.
  • This determines whether there are more digits to process.
23 BEQ PRINT ; If quotient is 0, print digit
  • If R0 is zero, it means this is the last digit.
  • Branches to PRINT to output the digit.
24 JSR PC, BTOA ; Recursive call with quotient
  • If R0 is not zero, it means there are more digits.
  • Recursively calls BTOA with the quotient in R0, continuing the process.

🧠 Summary

This block:

  • Extracts the least significant digit of the number.
  • Uses division and recursion to process digits from most significant to least significant.
  • Ensures digits are printed in the correct order by printing only after recursion unwinds.

Conclusion

Developing Creative Imagination in a structured way

Examples of the operators in sci-fi movies

Supersize me

  • Honey, I Shrunk the Kids (1989),

  • Honey, I Blew Up the Kid (1992)

Superman

Intelligence Enhancement

The Invisible Man


Time Travel

Anti-gravity

Capitan’s Log

Solve everyday issues with GenAI assistant

In this post I’d like to provide a short example of how chatbots, in particular Windows Copilot, can help you address issues related to web browsing, programming, reverse engineering, intelligent internet searching (aka semantic searching) etc.

The issue

In this case I wanted to check what sci-fi writer Pavel Amnuel had on his website. Even though that website looks dated and it is, the information it contains is still relevant to this day. There you can find his essays on hard science fiction, a “A Course of Lectures on TRIZ and the Development of Creative Imagination (PTB)” and more.

That course on Development of Creative Imagination consists of thirteen parts, and it turns out that the 11th one has incorrect encoding and looks like this at the time of writing

ÐÒ – ÝÒÎ Î×ÅÍÜ ÏÐÎÑÒÎ!

Ï.Àìíóýëü

Êóðñ ëåêöèé ïî ðàçâèòèþ òâîð÷åñêîãî âîîáðàæåíèÿ è òåîðèè ðåøåíèÿ èçîáðåòàòåëüñêèõ çàäà÷ äëÿ íà÷èíàþùèõ.
(Ïðîäîëæåíèå 11)


 òåêñòå èñïîëüçîâàíû íåêîòîðûå çàäà÷è ïî ÒÐÈÇ è ÐÒ èç êíèã è ñòàòåé Ã.Ñ.Àëüòøóëëåðà, Á.Ë.Çëîòèíà, À.Â.Çóñìàí è äðóãèõ àâòîðîâ.
 

ÝÒÈ ÔÀÍÒÀÑÒÈ×ÅÑÊÈÅ ÎÒÊÐÛÒÈß

Ìû ãîâîðèëè îá “îòêðûòèÿõ”, êîòîðûå äåëàåò ñàìà ïðèðîäà. Íî è â ÷åëîâå÷åñêîì îáùåñòâå íå îäíè ëèøü ðàáîòíèêè íàóêè ñîâåðøàþò îòêðûòèÿ. Íå íóæíî çàáûâàòü î êîíêóðåíòàõ – ïèñàòåëÿõ-ôàíòàñòàõ. Òîíêîñòÿìè íàó÷íûõ çíàíèé îíè âëàäåþò äàëåêî íå âñåãäà, íî ïðàâèëàìè ôàíòàçèðîâàíèÿ ïîëüçóþòñÿ êóäà ëó÷øå ó÷åíûõ.

How to fix it with GenAI?

So, what I did I’ve posted a part of it in Windows Copilot and asked about the encoding issue. It came up with a correct explanation right away.

prompt: fix encoding of this text …

response:
The text you’ve provided appears to be Cyrillic text misinterpreted as Latin characters due to incorrect character encoding. Most likely, it was originally written in Russian using Windows-1251 encoding, but then read or displayed using Windows-1252 (Latin-1) or UTF-8 without proper conversion.

🔍 Correct Encoding: Windows-1251 (Cyrillic)

When decoded properly, the text reads as:
РТВ — ЭТО ОЧЕНЬ ПРОСТО!
Г. Альтшуллер
Курс лекций по развитию творческого воображения и теории решения изобретательских задач для начинающих.
(Proverb 11)

В тексте есть некоторые задачи по ТРИЗ из РТВ, из книг и статей Г.С. Альтшуллера, Б.Л. Злотина, А.В.В. Асмана и других авторов.

🛠 How to fix encoding issues

If you encounter similar garbled text:

  1. Identify the original encoding — in this case, Windows-1251.
  2. Use a text editor or converter that allows you to change encoding (e.g., Notepad++, Sublime Text, iconv).
  3. Convert from Windows-1251 to UTF-8 to make it readable across modern systems.

Would you like me to help you convert a file or more text like this?


I’ve tried a couple of approaches, again, using Copilot’s assistance. In the end what I’ve ended up doing is saving the page as html file and updating the head element with the following meta tag below which provided correct Cyrillic encoding instead of the Latin one.

<meta charset=”windows-1251″>

This is how the properly encoded version looks like


I’ve also notified the author about this issue, and hopefully, by the time you are reading this post it will be fixed already.

Bonus

One more thing, if you’ve noticed the link to Pavel Amnuel’s website opens that page in English. This is no coincidence. The page is originally in Russian, but Copilot helped me to discover that Google Translate allows to translate a web page into a specific language and get a link to that translated page. How neat is that?


prompt: I mean I need a link that I can share after it was translated
response:
Ah, got it! You want a sharable link to the translated version of the page. Here’s how to do that using Google Translate:

✅ Create a sharable translated link

Use this format:
https://translate.google.com/translate?hl=en&sl=ru&u=https://milkyway2.com/amnuel/Rtv.htm
This link:

  • Can be shared with anyone — they’ll see the English version of the Russian page
  • Translates the page from Russian (sl=ru) to English (hl=en)
  • Automatically opens the translated version in Google Translate

By the way, while on that website you can right click on the mouse button and translate any of the articles into English. Nowadays, translations are of a very high quality.
Also, I saw that when you navigate to a translated page link, other linked pages are translated automatically!

Summary

Here you have it Windows Copilot or any other similar tool can do wonders if you ask it to help.

Reverse engineer anything with Large Language Models

In this post I’d like to share useful information on how to use LLMs and in particular Windows Copilot powered by GPT-4o (most probably) and GPT-5 models to assist in reverse engineering electronic boards.

So far, I was able to use these models to successfully reverse engineer software projects at work. And over the weekend I was able to apply Windows Copilot to help me reverse engineer a Switched-Mode Power Supply (SMPS) Board from a cheap DVD player I bought a couple of years ago.

The background for this hardware reverse engineering effort was that I bought a DVD player at Amazon to watch a couple of DVDs and listen to CDs I had. I used it a number of times and then didn’t use it for a while. When I tried to power it on a couple of years later it didn’t work. The debugging showed that the capacitor in the SMPS board was leaked. So, I found a similar capacitor (1000 uF, but 10 V max) in one of the old mobile phone charges and replaced it. The DVD started to work again. I’ve documented this process in the YouTube video. The main issue was that I didn’t check what was that capacitor’s maximum voltage. And as I’ve mentioned, it was 10 V. But other capacitors that were filtering the ripple before output were 16 V. I didn’t notice this at the time. So when I tried to use that DVD player later it didn’t start again. I already wanted to throw it into garbage, when I gave it a chance and opened it again. What I saw that the same capacitor that I replaced before leaked too. It turns out there is a need to use a 16 V maximum rated capacitor to account for potential voltage spikes.

This time I was more systematic and started to use Windows Copilot to query for what capacitor I could use in place the leaked one. I had a couple of old mobile phone charges left that I disassembled while looking for a 1000 uF capacitor which I didn’t found in the end. I only had 470 uF ones. But LLM reasonably suggested to use 1000 uF cap, since you can’t replace a capacitor without considering what was its purpose in the circuit. So, I understood that I must follow an advice from the Debugging Rules! book by Dave Agans, first I needed to Understand the System!

Since, I am an electrical engineer by education, I had some background to understand what various components were on the board and what some of them were responsible for. For example, I could see a rectifier bridge (it is used to convert AC current to DC), transformer, resistors, capacitors, chips and more. Which was helpful. If you have no such background, then before attempting a hardware reverse engineering project, you can use LLMs to learn the basics of electronics.

So, the board in question looks like below. First image shows the board from the top, and second image shows the board when it is placed on the lamp and it looks transparent to see the traces (wires) on the back side of it.

So, when you look at the left-hand side part of the left image you can see a white connector which connects to the AC power cord. Then it goes through the fuse just above it and connects to the black choke coils. It in turn connects to a bridge rectifier. Then it goes to a capacitor. After this I didn’t know what the circuit was doing exactly, though I could see a 8 pins Integrated Circuit (IC), a transformer with a yellow tape around it. More diodes, resistors, caps and a white output connector.

What was helpful was that the board had good markings explaining various components. This is a standard engineering practice. For example, R stands for Resistor, L stands for Inductor, C stands for Capacitor, D stands for a Diode, U stands for an Integrated Circuit (chip), Q stands for Transistor, J stands for a Connectors, F stands for Fuse.

I had an idea to upload an image of the board on the left in Windows Copilot and I did just that. GPT was able right away to tell that fuse was there, the transformer was there and it could recognize other parts too. It was also able to understand that it was a Switched-Mode Power Supply of a flyback type. So I started to provide it with information about the capacitor I wanted to replace, in particular that it was connected to the GND output pin. I also provided it with the pinout of the output connector and it was able to infer from it that there were two +5 V pins connected together which was correct.

But the most surprising part was that GPT was able to infer that there should have been a feedback loop implemented with optocoupler marked as PC817, which I was able later to identify on the board. Then it was able to infer that the 8 pin chip was most probably Pulse Width Modulation (PWM) controller and that it should have been connected to power transistor. Looking at the specification of that DM1203 chip I was able to confirm that it came with power transistor built-in shown in the diagram for the spec below.


In the end GPT taught me that the output from the PWM controller should be connected to the snubber capacitor

In the end after back end forth with the GPT it was able to provide me with the description of the schematics of the board.
Since I don’t have a history of my prompts at this time I tried to recreate in a concise manner my interaction with LLM. In the case below I provided two images and not one, and a detailed description of the board. LLM was able to exhibit very detailed understanding of what were the components on the board and how it worked.

Prompt:
I have the Switched Mode Power Supply board with following components PWM controller DM1203, optocoupler PC817, transformer with 12V and 5V output, smoothing capacitors at the output and the following pinout of the connector: -12V, GND, 12V, GND, +5V, +5V. Also attached come two images of the board: one front and one transparent that shows traces on the board. How about you provide me with the description of this board

Response from GPT-5
Board Overview

This is a flyback switched-mode power supply (SMPS) built around the DM1203 PWM controller IC. It takes AC mains input, rectifies and filters it, then uses a transformer to generate isolated DC outputs: +5V, +12V, and –12V. Regulation is achieved through an optocoupler (PC817) and a TL431 reference.

⚡ Input Stage

  • Fuse (F2AL250V): Protects against overcurrent.
  • NTC thermistor: Limits inrush current when first powered on.
  • Bridge rectifier (D9–D12): Converts AC mains to high-voltage DC.
  • Bulk capacitor (large electrolytic, ~220µF/400V): Smooths the rectified DC.
  • EMI filter (C1, C2, L1): Reduces conducted noise back into the mains.

🔋 Primary Side (High Voltage)

  • DM1203 IC: Integrated PWM controller + high-voltage MOSFET switch.
  • Transformer (EE-25 core): Stores energy during switch ON time, releases it to secondary when OFF.
  • Snubber network: A 10nF/1kV capacitor (103) in series with a 47kΩ resistor across the primary winding — absorbs voltage spikes caused by leakage inductance.
  • Startup/VCC capacitor: Provides supply to the DM1203 once oscillation begins.

⚙️ Secondary Side (Low Voltage Outputs)

  • Rectifier diodes: Fast recovery or Schottky diodes on each secondary winding.
  • Filter capacitors: Large electrolytics (e.g., 470µF/16V) smooth the DC outputs.
  • Inductors/ferrite beads: Further reduce ripple and noise.
  • Outputs provided:
  • +5V (two pins)
  • +12V
  • –12V
  • Ground (two pins)

🔁 Feedback & Regulation

  • Voltage divider (resistors): Scales the +5V output down to 2.5V.
  • TL431 shunt regulator: Compares scaled voltage to its 2.5V reference.
  • PC817 optocoupler: Transfers the error signal across isolation barrier to the DM1203’s FB pin.
  • FB pin capacitor (1nF–10nF): Stabilizes the feedback loop.

This ensures the +5V rail is tightly regulated, while the ±12V rails are “cross-regulated” (their accuracy depends on transformer design and load balance).

🧠 Functional Summary

  1. AC mains → rectified to ~300V DC.
  2. DM1203 chops this DC at ~65kHz into the transformer.
  3. Transformer provides isolated secondary voltages.
  4. Diodes + capacitors filter into smooth DC rails.
  5. TL431 + PC817 feedback loop keeps +5V stable.
  6. Snubber protects the switch from voltage spikes.

👉 In short: this board is a multi-output flyback SMPS designed for small electronic equipment, giving you isolated +5V, +12V, and –12V rails with the +5V as the regulated “master” output.

Would you like me to redraw this description into a clean block diagram (showing input → primary → transformer → secondary → feedback) so you can visualize the flow more easily?


You can tell that it’s quite amazing what LLM was capable of looking at the description above.

I’ve followed up and asked it to provide a block diagram too:

Prompt:
sure block diagram is good

Response from GPT-5:

Parting thoughts

So there you have it Windows Copilot using GPT-5 model in particular is capable of being a patient super skillful engineer that could help you with hardware reverse engineering on demand. You only need some basic understanding of the subject you’d like to explore and a curiosity to try new things.

Bonus

After I’ve replaced the leaked capacitor with a new one and the DVD player works again.

Long time no see

Recently, I’ve read the Remembrance of Earth’s Past trilogy by Chinese author Cixin Liu and was very much impressed by it. This in turn awakened my fascination with hard science fiction and development of creative imagination. What I mean by creative imagination development is a technique that was promoted by Genrikh Altshuller who was inventor, sci-fi writer and the creator of The Theory of Inventive problem Solving (TRIZ). To provide some context that creative imagination development technique was conceived by Altshuller with the help of his students, such Pavel Amnuel, who himself is a prolific si-fi writer and astrophysicist.

Since I am interested in topic of guided inventions which Genrikh Altshuller was written about I intend to write a number of post related to how hard sci-fi ideas can be purposefully engineered, using the tools of creative imagination development technique.

Stay tuned.

GPT provides some insight into how ketones’ loss happens

Image generated with Windows Copilot

Windows Copilot shines

The reply is below


🌟 Exploring Energy Loss During Ketosis: The Role of Acetone and Acetoacetate🌟

When our bodies enter ketosis—often due to low carbohydrate intake or fasting—we begin producing ketone bodies as alternative fuel sources. The primary ketone bodies are:

  • Beta-Hydroxybutyrate (BHB)
  • Acetoacetate (AcAc)
  • Acetone

While these molecules serve as vital energy sources, not all are utilized efficiently, leading to some energy loss. Here’s how it happens:


🔹 Energy Loss Through Ketone Excretion

1. Acetone Exhalation

  • Formation: Acetone is produced from the spontaneous decarboxylation of acetoacetate.
  • Excretion: Being volatile, acetone is exhaled through the lungs and also lost via urine and sweat.
  • Energy Implications: The exhaled acetone contains caloric energy that the body doesn’t recover—this represents direct energy loss.

2. Urinary Excretion of Acetoacetate and BHB

  • Renal Handling: The kidneys filter blood ketone bodies, reabsorbing most but not all. Excess ketones are excreted in the urine.
  • Energy Implications: The energy in these excreted ketones is also lost to the body. During high ketone production, urinary losses can be significant.

🔹 Key Research Findings

• Magnitude of Energy Loss

  • Quantitative Estimates: Energy loss through ketone excretion can range from 50 to 100 kilocalories per day in individuals in ketosis.
  • Influencing Factors: Depth of ketosis, metabolic rates, and kidney function affect the extent of ketone loss.

• Metabolic Adaptations Over Time

  • Increased Efficiency: With prolonged ketosis, the body adapts—kidneys enhance ketone reabsorption, and tissues improve ketone utilization, reducing losses.
  • Reduced Acetone Production: The body produces less acetone over time, minimizing exhaled energy loss.

• Clinical Contexts

  • Diabetes Mellitus: In uncontrolled type 1 diabetes, ketone production surges, and energy loss through excretion becomes more pronounced, contributing to weight loss.
  • Ketogenic Diets: Initial ketone losses are higher but tend to decrease as the body adapts to ketosis.

🔹 Understanding the Energy Calculations

• Caloric Content of Ketone Bodies

  • Beta-Hydroxybutyrate and Acetoacetate: Approximately 4.5 kcal per gram.
  • Acetone: While not a significant energy source, its loss still represents unused potential energy.

• Estimating Daily Losses

  • Urinary Ketones: Losing 10 grams of ketones via urine equates to about 45 kcal lost per day.
  • Exhaled Acetone: Though smaller in quantity, exhaled acetone adds to the total energy deficit.

🔹 Implications of Ketone Energy Loss

• Weight Management

  • Contributing Factor: Inefficient ketone utilization and subsequent energy loss may aid in weight loss by creating a caloric deficit.
  • Dietary Adjustments: Understanding this loss can help calibrate caloric intake for those on ketogenic diets.

• Metabolic Health

  • Efficiency Over Time: As the body adapts and reduces energy loss, dietary adjustments may be necessary to maintain weight loss momentum.
  • Monitoring Ketosis Levels: Regular testing of blood or urine ketone levels can inform about the state of ketosis and metabolic efficiency.

🔹 Additional Insights

• Breath Acetone as a Marker

  • Non-Invasive Monitoring: Breath acetone levels correlate with blood ketone levels, offering a convenient way to monitor ketosis.
  • Research Utilization: Used to estimate acetone production and associated energy loss.

• Ketone Metabolism Beyond Energy

  • Signaling Molecules: Ketone bodies play roles in gene expression, inflammation, and oxidative stress.
  • Therapeutic Potential: Minimizing unnecessary energy loss can enhance the benefits of ketogenic diets, especially in medical conditions like epilepsy or metabolic disorders.

🔹 Connecting the Dots

The loss of energy through acetone exhalation and acetoacetate excretion during ketosis, while seemingly minor, has meaningful implications:

  • Metabolic Efficiency: Highlights the balance the body achieves between utilizing alternative energy sources and conserving energy.
  • Dietary Planning: Emphasizes the importance of adjusting nutritional strategies as the body’s adaptation to ketosis evolves.
  • Health Outcomes: Offers insights that could improve interventions for metabolic diseases, weight management, and overall well-being.

Understanding the nuances of ketone metabolism and energy loss showcases the body’s remarkable adaptability! Whether for personal health goals or academic interest, delving into this area uncovers the intricate interplay between diet, metabolism, and energy utilization. 🌟


Ketosis with exogenous ketones cocktail

https://ketonutrition.org/the-many-faces-of-beta-hydroxybutyrate-bhb/?form=MG0AV3

Ketosis is just fifteen minutes away

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Photo by Igor Omilaev on Unsplash