# The New CAP Theorem on Blockchain Consensus Systems
## 2 Materials and Methods
### Related Work: Blockchain Consensus Tradeoffs  
[PERSON]'s CAP theorem in distributed systems has guided research in balancing Consistency, Availability, and Partition tolerance [10; 11]. However, the existing studies on blockchain consensus mechanisms often focus on specific aspects rather than on the inherent tradeoffs between them. While some works are addressing performance, security, and autonomy, this is often done fragmentally, in a KPI-specific approach, and does not focus on the interdependencies upon the attributes. Many of them are focusing on security and resilience issues, while others present comparative numeric analyses on KPIs. [PERSON] et al. in [15] provide a systematic review of blockchain consensus mechanisms, categorizing them based on their development and application requirements. The study of [PERSON] and [PERSON] in [19] emphasizes that no single mechanism can simultaneously optimize decentralization, security, and scalability, as \"the blockchain trilemma\". They formally analyze these, proving that different blockchain architectures must prioritize specific properties depending on the intended use case. In the context of Blockchain systems for the Internet of Things (IoT), [PERSON] et al. in [20] examine the suitability of various consensus mechanisms under resource-constrained environments. Their findings suggest that lightweight mechanisms, such as lightweight Byzantine Fault Tolerant (BFT) algorithms, enhance energy efficiency, but often sacrifice decentralization. [PERSON] et al. in [21] provide an overview of alternative consensus protocols, including hybrid approaches. [PERSON] et al. in [22] explore key performance indicators for blockchain consensus, evaluating their tradeoffs in computational complexity, security, and scalability. Their work underscores that the selection of a consensus mechanism depends on the application context, as different mechanisms exhibit strengths and weaknesses in different domains. [PERSON] et al. [23] focus on security vulnerabilities and attack vectors in blockchain consensus mechanisms, particularly in permissionless networks, where energy-intensive consensus can be more resilient against attacks. [PERSON] et al. in [24] proposed a reputation-based consensus mechanism built on information-centric networking to address fairness and efficiency concerns. Their findings suggest that incorporating reputation models can improve network security while maintaining consensus efficiency. From a sustainability perspective, [PERSON] et al. in [25] present a systematic literature review on energy-efficient blockchain consensus mechanisms, discussing strategies to reduce the environmental impact of blockchain networks. [PERSON] et al. in [26] present a comparative study of Proof-of-Work (PoW), Proof-of-Stake (PoS), and Hybrid consensus models. From the security perspective [PERSON] et al. in [27] examine Long-range attacks in PoS protocols, emphasizing the need for robust mitigation techniques. [PERSON] et al. [28] present a review of Blockchain consensus mechanisms in search of strong Sybil attack resistance, while [PERSON] et al. in [29] are assessing Blockchain consensus and security mechanisms against the 51% attack. [PERSON] et al. [30] evaluated the energy consumption of PoW-based blockchain networks, offering a comprehensive analysis of their environmental impact. Their findings highlight the ongoing debate regarding the sustainability of Blockchain technology. Several studies explore Blockchain efficiency. Entropy reduction in Blockchain consensus is investigated in [14], while [PERSON] et al. in [5] and [PERSON] et al. in [6] analyze the environmental impacts of the large-scale popular Blockchain systems rather than focusing on inherent constraints. This work differs by explicitly proving a fundamental tradeoff between Autonomy (A), Consensus (C), and entropic Performance (P) in the Blockchain consensus process.