An Entropy-Based Approach to Evaluating the Economic Efficiency of Cryptocurrencies

This work introduces an entropy-based framework for evaluating the economic efficiency of cryptocurrencies. Instead of measuring only price, market capitalization, throughput, or energy consumption, the paper proposes a composite index that captures how well multiple economic qualities are balanced inside a cryptoasset economy.

Context

Blockchain efficiency is often discussed in terms of transactions per second, latency, scalability, or energy consumption. Cryptocurrencies, however, are also economic systems: they have supply dynamics, user participation, transfer activity, wealth concentration, market value, and different forms of asset usage.

This paper focuses on that economic dimension. The central question is how to build a coherent index that can aggregate multiple on-chain and market-related attributes without reducing the analysis to one isolated metric.

The EB-index idea

The proposed Entropy Balance index uses Shannon entropy to measure how balanced a selected set of economic qualities is. Each quality is first normalized, then transformed into a probability distribution. Entropy is then used to quantify whether the selected qualities are concentrated around one dominant dimension or more evenly balanced.

pᵢ = rᵢ / Σ rᵢ

H(P) = - Σ pᵢ log(pᵢ)

Weighted version: H(P; W) = - Σ wᵢ pᵢ log(pᵢ)

Data and attribute sets

The illustrative evaluation uses on-chain data from Coin Metrics and compares six major cryptoassets: Bitcoin, Ethereum, Ripple, USD Coin, Dogecoin, and Cardano. The paper defines two different sets of attributes to show that the framework can be adapted to different interpretations of economic efficiency.

This distinction is important: the EB-index does not impose a single universal definition of economic efficiency. It provides a formal way to combine the qualities selected by the researcher.

Entropy results

The four plots below compare unweighted and weighted entropy for the two attribute sets. The unweighted version highlights balance among the selected qualities. The weighted version also accounts for the relative strength of the normalized attributes, changing the interpretation from pure balance to balance plus magnitude.

Unweighted EB-index — Set1

Set1 combines user activity with market-oriented indicators, showing how balance evolves across assets over time.

Weighted EB-index — Set1

The weighted version makes the index sensitive not only to balance, but also to the relative strength of the selected attributes.

Unweighted EB-index — Set2

Set2 focuses on dynamic qualities such as participation, transfer size, turnover, active supply, and wealth distribution.

Weighted EB-index — Set2

The weighted version changes the interpretation of the results by incorporating attribute magnitude into the entropy score.

Representative attribute distributions

The probability-distribution plots show how the selected qualities contribute to each asset's entropy score. They help explain why two cryptoassets can obtain similar entropy values for different internal reasons, or why the same asset can behave differently across Set1 and Set2.

Bitcoin

Set1

Bitcoin

Set2

Ethereum

Set1

Ethereum

Set2

USD Coin

Set1

USD Coin

Set2

Ripple

Set1

Ripple

Set2

Main contribution

• The proposed EB-index is designed to capture balance across selected economic qualities rather than relying on a single metric such as price, capitalization, throughput, or energy.
• The framework is customizable: researchers can select different attributes and weights depending on the economic behaviour they want to study.
• Set1 captures a compact view of activity and market-related behaviour, while Set2 focuses more deeply on user participation, transfer dynamics, supply usage, and wealth distribution.
• The weighted version of the index changes the interpretation by rewarding not only balance, but also stronger normalized attribute values.
• The work should be read as a methodological framework, not as investment advice or as a final ranking of cryptocurrencies.

Relationship with my broader research

This paper extends my blockchain evaluation work beyond protocol-level performance and energy analysis. While the DEBS and ICBC works study how blockchain systems behave under different network conditions, this work moves to the economic layer and asks how the internal behaviour of cryptoasset economies can be measured through a transparent, customizable, and theoretically grounded index.

Links and reproducibility material

The paper is accompanied by a public GitHub repository containing the normalized and entropy-derived datasets, documentation, citation metadata, and a plotting script for reproducing the main figures.