Entropy-Based Evidence for Bitcoin's Discrete Time Mechanism

TL;DR

This paper presents an entropy-based explanation for Bitcoin's discrete time mechanism, showing how proof-of-work maintains high entropy that collapses upon block discovery, with empirical analysis of propagation delays.

Contribution

It introduces an entropy-based interpretation of Bitcoin's temporal structure, highlighting the discrete collapse process and propagation dynamics across the network.

Findings

Block arrivals follow stable exponential patterns across difficulty epochs.

High-entropy proof-of-work state collapses upon valid block discovery.

Collapse propagation occurs over a finite, rapid interval in the network.

Abstract

Bitcoin derives a verifiable temporal order from probabilistic block discovery and cumulative proof-of-work rather than from a trusted global clock. We show that block arrivals exhibit stable exponential behavior across difficulty epochs, and that the proof-of-work process maintains a high-entropy search state that collapses discretely upon the discovery of a valid block. This entropy-based interpretation provides a mechanistic account of Bitcoin's non-continuous temporal structure. In a distributed network, however, entropy collapse is not completed instantaneously across all participants. Using empirical observations of temporary forks, we show that collapse completion unfolds over a finite propagation-bounded interval, while remaining rapid in practice.