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ARTEL 21: Bitcoin Energy
Chain Thermodynamics
Data Set:

Raw data sets are parsed directly from blockchain files. Per-block metrics (like T_nonce) are exact for each included block; cumulative metrics (like total energy) only sum the blocks in the selected data set.

Thermodynamic analysis of the entire Bitcoin blockchain. Inspired by the work of Bitcoin Lens.

View hypotheses derived from that paper →

Block Energy (Ublock)
Total Energy (Σ Ublock)
Cumulative sum only includes blocks in the selected data set. Sampled data sets skip blocks between samples, so values are lower than the true cumulative total. Use raw data sets for complete coverage.
Block Temperature (T_block)
Nonce Temperature (T_nonce)
Nonce Temperature (Gibbs Ensemble)
What this tells you: Shannon-weighted average of T_nonce across the chain. Blocks with higher Shannon entropy (more information per satoshi) contribute more weight. This is the expected nonce temperature of a randomly chosen bit from the ledger. The downward trend reflects decreasing T_block as the coinbase shrinks relative to cumulative supply.
Cumulative Nonce Temperature
Running sum of T_nonce across all blocks. Each block's contribution is T_nonce = p_block · H / ln(Ω), so early blocks with high p_block contribute more. The curve's shape reflects the evolving balance between Shannon information and Boltzmann multiplicity.

Conservation. Every block represents a transformation of energy into information. The Bitcoin network expends - of electrical power to produce a block every 10 minutes. This work is not wasted — it creates the thermodynamic basis for settlement finality.

2,099,999,999,755,528 sats. The fixed supply is the bounded phase space. Each block's coinbase selects a subset of this space, creating a measurable quantity of Shannon information: H = −p_block · ln(p_block), where p_block = coinbase / cumulative_supply. Accumulated across all blocks, this entropy is the thermodynamic signature of the chain.

Conservation identity. For any block t: ΔU_nonce(t) = ΔU_block(t). The resolution of a valid nonce and the creation of a block are not two processes but one thermodynamic event. Ublock = E_P · p_block · H, and Unonce = T_nonce · E_P · ln(D·2³²). Equating and canceling E_P gives T_nonce = p_block · H / ln(D·2³²).

Genesis block. At Genesis: p_block=1, H=0, T_block=1, T_nonce=0. The first block created no thermodynamic surprise and required no proof-of-work. Every subsequent block adds non-zero internal energy to the system. Accumulation of bits is accumulation of energy is accumulation of time.

Nonce Kelvin. T_nonce = p_block · (−p_block·ln(p_block)) / ln(D·2³²) is the exact temperature of an irreversible computational transformation. It equates the Boltzmann multiplicity of the nonce search to the Shannon information of the block it produces, scaled by the block's thermodynamic intensity p_block. This is the first quantity in physics that gives the temperature of computation from observables alone, without inference or thermal measurement.