Calculating Total Entropy

How total entropy accumulates in Qai Network.

From Single Blocks to Entire Chains

We’ve seen how PoEM measures the exact work in a single block. But how do we compare entire blockchains? This is where total entropy comes in.Think of it like this:

• Single block: “How hard was this math problem?”

• Entire blockchain: “How hard was this entire series of math problems?”

​Why Entropy Instead of “Work”?

Entropy is a physics concept that measures randomness or disorder. When miners find a block, they’re essentially reducing randomness by finding a very specific, ordered hash.The Key Insight: The amount of randomness removed (entropy reduced) directly corresponds to the energy spent creating that order.Real-world analogy:

• Messy room (high entropy) → Clean room (low entropy)

• Energy required to organize = Entropy reduced

• More organized = More energy spent = Lower entropy

​Geometric vs Linear: Why It Matters

Traditional PoW (Linear Addition):

• Block 1: 16 difficulty points

• Block 2: 16 difficulty points

• Block 3: 16 difficulty points

• Total: 16 + 16 + 16 = 48 points

PoEM (Geometric Multiplication):

• Block 1: Removes 1/65536 of possible states

• Block 2: Removes 1/65536 of remaining states

• Block 3: Removes 1/65536 of remaining states

• Total: (1/65536) × (1/65536) × (1/65536) = Much more security

Why Multiplication is Better:

• Exponential security: Each block makes the chain exponentially harder to recreate

• Real probability: Reflects the actual odds of recreating the work

• Better comparison: More accurately measures which chain required more total energy