Statistical Physics of Nakamoto Consensus : Phase Transitions and Thermodynamic Stability

The Nakamoto protocol is traditionally analyzed through the lenses of cryptography and game theory. We introduce a paradigm shift by demonstrating that the distributed Nakamoto consensus is fundamentally a dissipative structure maintained far from thermodynamic equilibrium. By mapping the macroscopic observables of the network to a mean-field Landau framework, we establish a falsifiable, physical foundation for blockchain immutability. We demonstrate that the emergence of a canonical history manifests as a continuous phase transition where time is not an a priori external clock, but an emergent thermal property strictly conjugate to irreversible heat dissipation. By coupling network power, latency, and block interval into an effective temperature, our model reveals a strict thermodynamic limit on the informational volume of bytes per block. Crucially, this limit transcends simple bandwidth constraints; it constitutes an irreducible thermal bound dictated by the computational validation latency of the silicon substrate, which prevents topological collapse via a Kosterlitz-Thouless transition. Furthermore, we recontextualize the Unspent Transaction Output (UTXO) set as a Markov blanket required to dissipate spatial Shannon entropy, and show that deterministic step-functions in the exergy injection rate (the protocol's ''Halving'') function as first-order thermodynamic quenches. In this non-equilibrium regime, the network's violation of the fluctuation-dissipation theorem is dynamically stabilized through the continuous expenditure of exogenous exergy.