The idea that an agent could not do otherwise in exactly the same circumstances is considered a problem facing both libertarians and determinists.

Information philosophy has a particular importance for this question, because it can be asked whether exactly the same information could ever be present at two different locations in the universe of space and time.

Surprisingly, in the classical mechanical deterministic universe all moments of time contain exactly the same information, since complete knowledge of the universe at any time implies the exact situation at all other times, past and present.

Perhaps equally surprising is the fact that in our expanding universe where information is being destroyed with the increase in entropy, and simultaneously new information is being created - sadly somewhat less than the increase in disorder - we can say that the exact same circumstances never occur.

This dramatic difference is one of the most outstanding disproofs of the metaphysical idea of physical determinism.

That the exact same circumstances never occur is nowhere more clear than in systems that clearly store the increased information and so exhibit a record of the change in the universe. Astrophysical objects show signs of their evolution. The geological record of the earth's surface displays a rich past. Most living organisms have encoded traces of their lives. And of course human beings carry a part of their past in their memories.

So, like many philosophical problems, the idea of "exactly the same circumstances" reduces to the practical problem of being in very similar circumstances, which is still an interesting question.

Libertarians who think they require a sort of extreme "metaphysical freedom" have argued for what some call a "dual power" to make a rational decision to do something different in exactly the same circumstances.

Peter van Inwagen somewhere wrote about a thought experiment where God reset the circumstances to be the same, and he imagined the outcome of free decisions which had intrinsic unpredictability because they were indeterministic. Van Inwagen argued that there would be a statistical distribution of outcomes, as the agent did different things following the distribution of indeterministic causes. [get the reference]

Although this is consistent with those who think that indeterminism directly affects our actions, it is not at all what our Cogito model suggests. Indeterminism affects only the alternative possibilities available to the agent for choice. These alternative possibilities are likely to vary from circumstance to circumstance, making the agent unpredictable.

But assuming for the sake of argument that identical alternative possibilities came to mind, the Cogito model predicts that the agent will make the same determination based on character and values. Those libertarians who want something different to happen have an antipathy to determination like that William James found in determinists with their antipathy to chance.