The most inventive idea ...[is]...the distinction between three different types of money: fast, medium, and slow. Fast money is what we would recognize as cash, issued by a planetary government. Medium money is a way to denominate assets that can't immediately be converted into cash, like real estate. It's not a new observation that as assets these aren't effective for interstellar trade. Cash or property from another star system isn't worth all that much without faster-than-light travel, since by the time you manage to get there, the cash might be inflated into worthless paper and the house might have burned down. What Stross adds to these two familiar asset types is slow money, a currency that's backed by the wealth of an entire star system and whose transactions must be signed by trusted third parties, which is to say, other star systems. That's where the "slow" part comes in: slow money transactions take years to complete because signals must cross interstellar distances before they can become valid. Like a normal currency, a star system's slow dollars can inflate or deflate in value, but the glacial transaction speed means someone owning slow money can trust that circumstances won't run out of control before they hear about it. Crucially, this allows slow money to be used to denominate debt held across star systems.
For several decades now hard science fiction has struggled with the dispiriting energy requirements for space travel. Formerly the subgenre of techno-optimists who fervently believed in humanity's manifest destiny to conquer the stars, it has become increasingly difficult for its authors to figure out how to make the financial numbers add up just for colonizing the solar system, much less the brutal expanse of interstellar distances. In that context, Neptune's Brood paints a heartening future where an undaunted "humanity" spreads itself ever further in a wave of colonization that actually accelerates over time, but the reasoning is interesting and, to my knowledge, completely new. Colonizing another star system is such a stupendously expensive enterprise, we learn, that the only way the colony can hope to pay back its "debt of initiation" to its mother system is to launch colonies of its own and require payment of similar debts from them. Another contributing factor is the unchecked concentration of wealth, which has created a tiny elite who are wealthy beyond imagining. Their fortunes, one character asserts late in the book, "can only be realistically be depleted by the founding of a new solar system or two."