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.

翻译：智能系统的研究从经济理性的角度解释行为。这导致了一个涉及函数或效用的优化原理，即系统将演化直至达到效用最大的配置。近年来，该理论引入了约束条件，即在满足某些信息处理约束的同时最大化效用时达到最优。这让人联想到热力学系统。因此，智能系统的研究受益于热力学的工具。本论文的第一个目标是阐明这些结果在智能系统研究中的适用性。我们可以将热力学或智能系统中的局部转移步骤视为由不确定性驱动。事实上，这两个系统中的转移都可以用优超关系来描述。因此，诸如香农熵之类的实值不确定性度量仅仅是其更复杂行为的代理。更一般地说，实值函数对于研究包括经济学、热力学和量子力学在内的多个主题的序论方法中的优化和复杂度至关重要。本论文的第二个目标是改进这一分类。热力学系统与智能系统之间的基本相似性基于由预序表达的不确定性概念。我们也可以将计算过程步骤中的转移视为决策制定程序。事实上，通过对所考虑的序结构添加一些要求，我们可以构建一个不确定性减少的抽象模型，该模型允许纳入可计算性，即区分可以通过遵循有限指令集构造的对象与不能构造的对象。本论文的第三个目标是阐明允许此类框架的序结构所需的要求。