  The study of intelligent systems explains behaviour in terms of economic
rationality. This results in an optimization principle involving a function or
utility, which states that the system will evolve until the configuration of
maximum utility is achieved. Recently, this theory has incorporated
constraints, i.e., the optimum is achieved when the utility is maximized while
respecting some information-processing constraints. This is reminiscent of
thermodynamic systems. As such, the study of intelligent systems has benefited
from the tools of thermodynamics. The first aim of this thesis is to clarify
the applicability of these results in the study of intelligent systems.
  We can think of the local transition steps in thermodynamic or intelligent
systems as being driven by uncertainty. In fact, the transitions in both
systems can be described in terms of majorization. Hence, real-valued
uncertainty measures like Shannon entropy are simply a proxy for their more
involved behaviour. More in general, real-valued functions are fundamental to
study optimization and complexity in the order-theoretic approach to several
topics, including economics, thermodynamics, and quantum mechanics. The second
aim of this thesis is to improve on this classification.
  The basic similarity between thermodynamic and intelligent systems is based
on an uncertainty notion expressed by a preorder. We can also think of the
transitions in the steps of a computational process as a decision-making
procedure. In fact, by adding some requirements on the considered order
structures, we can build an abstract model of uncertainty reduction that allows
to incorporate computability, that is, to distinguish the objects that can be
constructed by following a finite set of instructions from those that cannot.
The third aim of this thesis is to clarify the requirements on the order
structure that allow such a framework.
