Can a Liquidity Pool Experience “Impermanent Gain”?

No, a liquidity pool cannot experience "impermanent gain" in the technical sense of the term. Impermanent loss is defined as the difference between the value of the deposited assets and the value of simply holding them.

This difference is always zero or negative (a loss) because the AMM always forces the pool to hold more of the relatively depreciating asset, which is mathematically less optimal than holding the original assets.

Why Is the Option Premium Always Greater than or Equal to Its Intrinsic Value?
What Is Impermanent Loss and How Does It Relate to Providing Liquidity?
Does an In-the-Money Option Experience Less Time Decay than an Out-of-the-Money Option?
Can a Stablecoin-to-Stablecoin Liquidity Pool Experience Impermanent Loss?
What Are the Implications of a Team Holding All Tokens under a Simple Lock-up versus a Vesting Schedule?
In What Scenario Would an Initial Margin Requirement Be Lower than the Maintenance Margin?
What Is ‘Impermanent Loss’ for a Liquidity Provider in a Smart Contract-Based DEX Pool?
Can Impermanent Loss Be Positive, Resulting in an Impermanent Gain?

Glossar