Adequate levels of arousal can induce positive emotions, while high potential for arousal can induce negative emotions. To explain the effects of arousal on emotional valence, we propose a new mathematical framework of potential variations of arousal in the dual processes of human cognition: automatic and control processes. Models have been proposed to explain emotion in a dual process, but few suitable mathematical formulations have been found. Our model relates free energy to the likelihood of arousal and its changes to explain emotional valence. As a result, decreasing and increasing free energy induces positive and negative emotions, respectively. We formalize the transition from automatic to controlled processes in the dual process as a modification of the Bayesian prior distribution. We model the emotional valence using the free energy increase (FI) when trying to modify the Bayesian priors and its decrease (FR) when successfully recognizing the same stimulus with the modified priors, Define three emotions: “interested” and “confused”. ‘ and ‘boring’ variations. A mathematical analysis comparing various Gaussian model parameters suggests that: Always increase FR. Describes the association of outcomes and emotions in controlled processes. Mathematical models provide a general framework for predicting and controlling emotional valence in dual processes that vary with viewpoint and stimulus, and are for understanding discrepancies in the effects of arousal on valence.
