Minecraft entity collision logic (simplified)

applyEntityCollision.java

public class Entity {
	public void applyEntityCollision(Entity other) {
		double dx = other.posX - this.posX;
		double dz = other.posZ - this.posZ;
		double largestDistance = Math.max(Math.abs(dx), Math.abs(dz));
		if (largestDistance >= 0.01) {
			double vx = dx / 20;
			double vz = dz / 20;

			if (largestDistance < 1) {
				vx = vx / Math.sqrt(largestDistance);
				vz = vz / Math.sqrt(largestDistance);
			} else {
				vx = vx / largestDistance;
				vz = vz / largestDistance;
			}

			this.xVelocity = this.xVelocity - vx;
			this.zVelocity = this.zVelocity - vz;

			other.xVelocity = other.xVelocity + vx;
			other.zVelocity = other.zVelocity + vz;
		}
	}
}

Entities can also have custom hitbox sizes: https://docs.microsoft.com/en-us/minecraft/creator/reference/content/entityreference/examples/entityproperties/minecraftproperty_collision_box