1. The engine Carnot imagined
In 1824 Sadi Carnot asked how much work any heat engine could ever deliver. His answer: it depends only on the gap between the hot side and the cold side. His ideal engine runs a loop of four strokes and ends exactly where it began.
The shaded loop is the work done in one cycle. Widen the gap between the reservoirs and the loop grows. Close it and the loop disappears.
How the book maps it onto mining
Demand is the hot reservoir: it arrives from outside and does not care what a coin cost to make. The cost of production is the cold reservoir: the energy below which a coin cannot be minted. Hashrate is the working substance, swelling as heat enters and shrinking as it leaves. The output is security and a trustworthy record, paid for in energy nobody can fake.
Carnot's efficiency formula translates almost literally. Replace temperatures with price and cost, and 1 minus cost over price is the miner's margin. A market bottom is the engine stopping: price has fallen to cost and there is no gap left to work across. The matching of the four strokes to the book's four market phases is our reading, not a claim the book makes stroke by stroke.
Where the analogy stops
A real Carnot engine is slow, reversible and runs between fixed reservoirs. The mining cycle is none of those. Machines take months to arrive, which is why it overshoots both ways; the book notes that an instant response would never overshoot, and there would be no cycle. And the cold reservoir does not stay put: each loop leaves the cost of production higher. That drift is the second half of the book's subtitle, Brownian global, covered in part 5.
2. What a coin costs to make
The book's floor is three physical quantities multiplied together. Nothing in it is opinion. The small charts show how each has moved since the ASIC era began in late 2023.
Hashes per coin is the network's hashrate divided by what it issues each second. Joules per hash is the blended efficiency of the machines doing the work, which the book calls the workhorse. The price of a joule is the network-average electricity price, including cooling and losses.
The book treats a machine as energy paid in advance: its cost should be spread across every coin it will ever mine. Here is the all-in cost for a new KS7, the current workhorse, bought today.
Assumes hashrate and price stay where they are while issuance keeps falling each month, so energy per coin rises over the machine's life. The book says a machine's life ends when its resale value reaches zero, and the used market sets that date.
Today's floor for each pairing of fleet efficiency and power price. Colour shows where today's price sits against it.
3. Price against the cost to make
Above the floor, price is opinion. The shaded band runs from an efficient miner on cheap power to an older machine on dear power. Where price sits relative to that band is the most useful single reading in the book.
The coloured strip under the chart is the market phase from part 4. The floor is drawn from mid-2023; before that, GPUs mined Kaspa alongside other coins, so their energy cannot be cleanly assigned to it.
Each peak multiple has been lower than the one before, which is what the book predicts: every gap is smaller than the last.
4. Where we are in the cycle
The book names four phases from two questions. Are coins getting dearer or cheaper? Is hashrate growing or shrinking? Plot one against the other and the market traces a loop through four quadrants.
Changes are measured over the cycle window set in Model settings, using 7-day averages. Short windows catch turns early but flicker; long windows are steadier but late.
5. Carnot local, Brownian global
Each loop looks like the last, but the floor underneath climbs. The book borrows Feynman's ratchet: random jiggling that can only move one way. Feynman's version fails because nothing pays to hold the pawl. This one works, because sunk machines and patient holders hold it, and energy pays for that every day.
Two ratchets
The machine ratchet. Hardware bought in a hot phase is sunk. When price falls, machines are parked rather than scrapped, and they come back when price returns. The network's capacity to do work does not fall back to where it started.
The coin ratchet. Each cycle, more coins end up with holders whose cost base is higher and who will not sell below it. The book calls the resulting resistance a wall of opinion.
Why efficiency does not undo it. Better machines cut the energy per hash. But they attract more competition than they displace, and issuance keeps thinning, so each coin ends up carrying more energy, not less. The chart below shows it happening.
Cost to make a coin on the day of each year's lowest close (2023 from mid-year, when the floor becomes meaningful). The ratchet shows as higher lows across cycles, although the floor can ease within a downturn as the least efficient machines switch off.
The highest multiple reached each year. Shrinking gaps mean the engine runs cooler as it matures.
Both lines start at 100 in October 2023. Efficiency improved about fourfold while the energy behind each coin rose many times over. Economists call this the Jevons effect; the book reaches it from first principles.
6. A power law from physics
Most crypto power laws are curve fits to price. This one is fitted to the cost of production and anchored at a cycle bottom, because the book says that is where the floor shows itself. The result rises with time, but ever more slowly, which is exactly the shape of shrinking gaps.
Fair value is the floor times the multiple set above. The hot line is twice fair value, where past cycles have stalled.
7. Inside the mines
The floor is set by real machines on real power contracts. These views show who is making money, who is under water, and how much of what they mine they have to sell.
Each block is a machine class. Its height is the electricity price at which it just breaks even today; its width is its share of hashrate. Blocks below the power line are losing money on every hash. The mix is illustrative: adjust it to your view of the fleet.
The share of newly mined coins that must be sold just to pay the electricity bill. Above 100%, even selling everything does not cover power, and machines switch off. Because the amount mined halves every year, this forced selling shrinks over time.
Simulated day by day for three years with monthly emission cuts. When a day would lose money the machine is parked, as the book describes, and restarts when it pays again. Prices other than the KS7 list price are placeholders; enter your own.
8. Energy and security
What the engine consumes, and what it buys. For an energy audience, this is the section that matters: the network is a large, flexible, price-responsive load that switches off when margins vanish.
Kaspa's issuance halves every twelve months in twelve smooth monthly steps, rather than in sudden halvings. Every monthly cut raises the energy behind each new coin unless hashrate falls at the same pace.
9. Ideas from the book
The concepts behind the charts, in plain words.
- Carnot local, Brownian global
- Over one cycle the market behaves like a heat engine and returns to its starting shape. Across many cycles it behaves like a ratchet that only turns one way.
- The workhorse
- The cost of production is set by the machine that wins on total cost and so does most of the work. Not the newest machine, and not the average one. It is always a chip in a location under a power contract.
- Floor and wall
- The lower bound on price is physics: energy, efficiency and the work behind each coin. The upper bound is a wall of opinion, set by what holders paid and what they expect.
- Joules per hash, joules per coin
- Better silicon lowers the energy per hash. It draws in more competition than it displaces while issuance thins, so each coin carries more energy.
- Capex is prepaid energy
- Building a machine consumes energy that should be spread across every coin it mines. Its working life ends when its resale value reaches zero.
- Time, the second currency
- Mining spends only energy and time. Paying a premium for a machine buys time, and the premium is the exchange rate between the two.
- Parked, not scrapped
- In downturns machines are switched off and stored, then return quickly when price does. The fleet behaves like flexible, price-responsive demand on the grid.
- The railroads
- Investors can lose their money while the infrastructure they paid for stays in place and keeps working.
- Seller of last resort
- The electricity bill never pauses, so miners keep selling when nobody else will. That forced selling is capped by issuance, which shrinks every year.
- Decentralisation breathes
- Wide margins let dearer power and older machines join, spreading hashrate across more places. Cold phases concentrate it on the cheapest power, but each time a little less.
- Fees
- A fee means the same joules put more coins in the miner's hands. Fees track usage, and a sustained fee market still ends up as hardware, feeding the ratchet.
- What the book leaves open
- Whether fees can replace issuance, whether demand keeps a lasting floor, and whether competition keeps outrunning efficiency. The book separates what has been observed from what has only been reasoned.
10. How this is built
The floor. Cost to make one KAS = hashes per KAS × fleet joules per hash × electricity price. Hashes per KAS is daily network hashrate divided by emission per second.
Data. Hashrate: daily snapshots from the public Kaspa REST API. Price: daily closes from Yahoo Finance (KAS-USD) from June 2022. Emission: Kaspa's chromatic schedule, 440 KAS per second at its start in May 2022, cut by the twelfth root of two each month; it reproduces the live block reward. Supply is calibrated to the API's circulating supply on the snapshot date.
Assumptions you should question.
- Fleet efficiency is a judgement, not a measurement: roughly 150,000 J/TH in the GPU era, falling through FPGAs to about 450 J/TH for early ASICs, 190 for the KS5 class and 110 for today's KS7-heavy fleet. The Model setting scales the whole timeline.
- Electricity defaults to $0.055/kWh all-in as a network average. Real miners range widely.
- The cost band runs from 75% of fleet energy use on 70% of the power price, to 130% on 130%.
- The power law is anchored on the lowest close of the 2026 downturn (13 August 2026). An exponent near 2 is supported by a regression on the floor, a bottom-to-bottom estimate and a plain price fit, but only a few cycles exist.
- Before mid-2023, GPUs mined Kaspa alongside other coins, so early floors are not meaningful.
- Fees are ignored as small relative to issuance. Machine prices other than the KS7 list price are placeholders.
What this is not. A cost-of-production model explains where support should be, not where price will go. The book is explicit that everything above the floor is opinion. Nothing here is investment advice.
Credit. All concepts are from Satoshi's Engine: Carnot local, Brownian global by Moose.kas, summarised in our own words. The stroke-by-stroke Carnot mapping, the fitted power law and the market data work are this page's additions, not the book's.