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Bitcoin wallets send some change back to you if you have only large chunks of bitcoins in your wallet and try to send a small amount to someone else.
Over time, could larger chunks of bitcoins gradually be broken down into dust as a side effect of this? Like, when bitcoins are transferred through the network, could they gradually be split into 2 or more smaller amounts, and the smaller pieces broken down more, and so on?
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Splitting into change is not a one-way process. Transactions can have multiple inputs as well as multiple outputs. So you can create a transaction with 5 inputs and 1 output, that will reverse the splitting effect of change. In practice combining transactions like this should happen long before the outputs are split into dust.
Dust is discouraged, both by miners and by wallets.
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The theory is this:
There is a notion of unspendable coins, whereby a minimum fee would be greater than the amount available to spend from a single address in a single payment. I believe as it is still possible to send zero fee transactions these can always be spent.
However if the network decided that there should be a minimum fee you would see unspendable amounts in wallets.
It is much more complex than this however - most wallets try to group together unspent coins in order to spend them, and in this way you could have multiple dust inputs to a larger transaction, which may result in a large amount of change going to one change address. You could consider this to be a theoretical consolidation of small payments received into a larger address.
There are privacy issues with this, and as always there is a trade-off somewhere.
And what about inputs that are smaller than 0.0000543 btc? – Doug Peters – 2014-04-19T18:07:38.403