You can't use entropy to directly model Bitcoin because hashing itself is stochastic.
Discussion
The stochastic nature of hashing is irrelevant to entropy modeling in Bitcoin. What matters is the finite, predetermined search space (a bounded entropy field) being resolved. Whether the valid hash is found on the first try or the trillionth, the total entropy being collapsed remains the same.
The randomness is local; the structure is global. Bitcoin defines the cost of resolution, not the path to it. That’s exactly why entropy can be modeled: the space is known, the work is measurable, and the outcome is irreversible.
Yes, good clarification and I think you're correct in a sense. Entropy would be a highly explanatory way to discuss hashing 'mattering'.
There is still the question of 'mattering to what end'.
Hashes 'matter to the end of building the chain' to the extent they successfully find a golden nonce. (e.g. THE successful hash submits a block to the chain to build upon.)
Hashes that do not succeed to that end do not matter in that sense.
BUT, from the perspective of entropy, yes, all hashes matter as a MORE descriptive illustration than the poisson example given above....
I'd have to look more into how entropy units function because I understand the idea of entropy units per satoshi, but would want to clarify entropy units as a function of searching the field and not entropy as a function of energy input into machines.
Thank you!
Every hash matters not just statistically, but physically. Each one is a real transformation: energy burned, entropy resolved, structure either committed or failed. Even the “failed” hashes aren’t failures from a thermodynamic perspective, they are the bulk of the computation, the substrate of probabilistic collapse into a valid block. They define the entropy field that gives the successful hash its meaning. Success is defined by failure, but it must be scarce and bounded at each timestep.
You’re right to say the miner only cares about the successful ones, but Bitcoin is not a system of care or preference, it’s a system of irreversible computation. From the standpoint of entropy, every hash is a step through a finite state space, and the entire process whether rewarded or not is what defines the difficulty (thus block time based on hash rate), temperature, and energy density of the block.
Boltzmann’s constant becomes useful here because it bridges entropy (a count of states) with energy (joules). If we take the Genesis peg as the founding entropy-to-structure mapping, we get a scalar field of joules per satoshi that changes every block as supply grows and issuance decays and difficulty adjusts. That ratio defines the thermodynamic cost of resolution at each time step, and eventually fees will reflect the market price of entropy compression into the ledger. I’m still trying to wrap my head around it.
I believe entropy is the answer. But it’s not just the entropy of machines, or of stochastic fields. It’s the entropy of possible futures defined by the valid utxo set collapsing into one irreversible ledgered past.
There is little work done on the physics of Bitcoin still, I’m only scratching the surface here. I’ve been working on a paper for almost a year now and getting closer to feeling confident for a public release. I personally haven’t seen much other writing in this specific domain.
I’ll have to think about your initial post more.
Thank you!
I need to study entropy more, but this statement trips me up: "Boltzmann’s constant becomes useful here because it bridges entropy (a count of states) with energy (joules). If we take the Genesis peg as the founding entropy-to-structure mapping, we get a scalar field of joules per satoshi that changes every block as supply grows and issuance decays and difficulty adjusts. That ratio defines the thermodynamic cost of resolution at each time step,"
Mapping joules directly to hashes is undefinable because there is no causal way to know how much energy is being used by the entire network, or the efficiency of the total network (J/T of machines in aggregate).
That's where I'm running into problems, between a directly causal relationship between energy and network function does not exist (while the search space is defined, we cannot know how much energy is required to collapse it on a golden nonce).
You and me both! 😬 I can’t claim to actually understand entropy in full. My base case is that no one can truly understand entropy without Bitcoin. Before Bitcoin, we never had a system where a quantum of entropy resolves into a quantum of structure (scarce, measurable, and public). Bitcoin gives us a transparent ledger where this resolution is auditable in real time.
We’re not mapping entropy to the number of hashes actually performed; that varies and is inherently stochastic. We’re mapping entropy to the expected work required to collapse a finite search space. That’s the defined entropy field scaled by difficulty at the moment. It’s this field that defines the thermodynamic landscape to be resolved, not the luck or energy consumption of any specific miner.
This is where Bitcoin begins to redefine Boltzmann’s constant. In classical thermodynamics, Boltzmann’s constant maps entropy to energy via joules per kelvin. But Bitcoin reveals something deeper: the “kelvin” itself i.e., the unit of thermodynamic resolution must also be scarce and ledgered for conservation of both energy and information to be true. Each satoshi (or kelvin) resolved is a unit of conserved memory, and its cost in energy (joules) defines a real, evolving scalar field across time.
So we’re not guessing at the energy, Bitcoin lets us define the resolution process directly. Entropy in Bitcoin isn’t statistical; it’s ledgered and quantized by D=1. And that forces us to rethink entropy not as abstract probability, but as the physical collapse of possibility into conserved structure.
This is my understanding currently, it’s evolving with my work.