Nakamoto Distributed Consensus as a Non-Equilibrium Phase Transition : A Phenomenological Statistical-Physics Description

Moving beyond traditional cryptographic and game-theoretic analyses, we model Nakamoto consensus as a dissipative structure maintained far from thermodynamic equilibrium. By mapping macroscopic network observables onto a one-dimensional Ginzburg--Landau framework, we propose a falsifiable phenomenological description of blockchain immutability grounded in non-equilibrium statistical physics. In this description, the emergence of a canonical history appears as a continuous ordering transition, and time is treated not as an externally imposed global clock, but as an emergent coarse-grained variable driven by irreversible dissipation. By coupling network power, latency, and block interval into an effective temperature, the model yields a protocol-dependent upper bound on the informational volume of bytes per block ($V_{\mathrm{B,crit}}$) and anchors the ledger's macroscopic stability in the embodied exergy of the physical hardware substrate. In particular, computational validation latency ($\gamma$) imposes an irreducible constraint even in the formal limit of infinite communication bandwidth. We further interpret the Unspent Transaction Output (UTXO) set as an effective Markov blanket providing a compressed state description, and we analyze deterministic subsidy step changes (the protocol's ``Halving'') as non-equilibrium thermodynamic quenches. Within this framework, the observed dynamics are consistent with a persistent violation of the fluctuation--dissipation theorem, maintained by the continuous expenditure of exogenous exergy.