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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).

Jack K 4mo ago

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.

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