# The New CAP Theorem on Blockchain Consensus Systems
## 5 Discussion
### Empirical Validation Through Real-World Data
In Table 1, we see the Number of reachable peer Nodes (N), the Nodes Participating in the initial Consensus requirement (W), the target Transaction Time and the time to Finality, the Average Transaction size, and the Energy Consumption per Transaction (kWh), of Bitcoin (PoW), Ethereum 2.0 (PoS), Hyperledger Fabric 3.0 (Raft, PBFT), and IoT micro-Blockchain at the time of the writing. The estimation of the Entropic Performance (P) bit/kWh is based on macroscopic benchmarking data [18; 34; 35]. In every transaction, (\(W\cdot Average\)\(Transaction\) size) bits are entering finality, at the cost of _Energy Consumption per Transaction_ kWh. As we see, the Bitcoin Blockchain, which mandates the maximum \(W\), also presents the higher Transaction time and the lowest entropic Performance of all. On the contrary, the Ethereum and the Hyperledger Fabric, which operate in lower \(W\), are significantly faster and present much higher entropic Performance (ranking \(10^{4}\) and \(10^{3}\) less than Bitcoin, respectively). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  
* The data summarized in Table 1 falls beyond the core scope of this work and are given as a reference to the reader. **Estimations at the time of the writing.**  
\end{table} 
Table 1: Benchmarking the entropic Performance of large-scale Blockchain systems *. The considerations of the above empirical analysis are summarized and presented in Table 2 with respect to (A), (C), and (P). In Table 2, a comparison of the large real-world systems (Bitcoin (PoW), Ethereum 2.0 (PoS), and Hyperledger Fabric 3.0 (Raft, PBFT) with respect to Autonomy (A), Consensus achievement (C), and entropic Performance (P) is presented). As we see, the high consensus achievement requirement of Bitcoin (high \(W\)) leads to low entropic Performance, while the low Consensus achievement requirement of the Hyperledger Fabric results in a significantly high entropic Performance. The Ethereum 2.0 balances (A) and (C) to achieve high entropic Performance (P). In all cases, the _new CAP theorem_ holds strong: of the (A), (C), and (P), two at the most are optimized. The real-data benchmarks fully comply with the _new CAP theorem_. Given the above, someone may easily conclude that the calculation of the precise entropic Performance of the various Blockchain systems is subject to a vast number of factors, and architectural- and implementation-specific considerations, as well as to the co-evaluation of the dynamic real-world conditions. These are susceptible to further thorough refinement through in-depth modeling and analysis of each Blockchain system. Still, as illustrated, the revealed mutual exclusions persist firmly in massive scale systems of thousands of nodes. In large-scale Blockchain systems with thousands or millions of peer nodes, the relationships between (A), Consensus (C), and (P) are expected to exhibit non-linear behaviors. The detailed formal analysis of the large-scale Blockchain systems is out of the core scope of this work and remains a subject for future works. Following in the next sections, we discuss the implications of the theorem in the large-scale real-world systems.