You’re describing only the local thermodynamic outcome of a failed miner (heat) while ignoring the global thermodynamic structure that Bitcoin mining actually operates inside.

A solo rig that never finds a block contributes no local informational change. Yes we both agree here, but it absolutely does tehcnically contribute to the global entropy field set by the difficulty target. That difficulty defines a Boltzmann entropy surface over the 32-bit nonce space. The expected energy for a valid block is determined by that landscape, not by any individual machine’s waste heat.

This framing only accounts for dissipation, not for the fact that difficulty predefines the energy budget required for a valid state transition by quantizing the search space. This entropy field exists independently of any miner; it is the global thermodynamic environment into which miners inject work. A valid block header is a statistically rare microstate. It is the structured residue of the dissipated work and that is precisely why nodes can validate it instantly: the improbability is preserved in the structure.

Yes a failed solo miner’s energy becomes heat, but the network’s energy budget (the real cost of producing one improbable, verifiable microstate) is governed entirely by the thermodynamics of the difficulty field. Until you account for that, you’re not describing the whole system and the underlying transformation.