Introduction
The main positive symptoms of schizophrenia, namely hallucinations, word salad, and loosening of associations, all seem to be variations of the latter, so loosening of associations will here be taken as the primary disorder. Stress and the brain's dopaminergic system are strongly implicated in the causation of schizophrenia. In connection with stress, psychologists speak of "the affective [emotional] pathway to schizophrenia."
Organismal responses to stress
Stress is known to increase genetic variability in bacteria, a process known as transformation. Stress is likewise known to increase the meiotic recombination rate in sexually reproducing organisms such as fruit flies. (Stress-induced recombination and the mechanism of evolvability. Zhong W, Priest NK. Behavioral ecology and sociobiology. 2011;65:493-502.) It seems that when an organism is in trouble, it begins casting about ever more widely for solutions. If evolution is the only mode of adaptation available, this casting about will take the form of an increase in the size and frequency of mutations. In conscious humans, however, this casting about in search of solutions in the face of stress may well take the form of a loosening of associations during thought. Should the person find the solution he or she needs, then presumably the stress levels go down and the thought process tightens up again, so we have a negative feedback operating that eventually renormalizes the thought process and all is well. In optimization theory, this process is called "simulated annealing."
Disorder of a cognitive stress response
But what if the person does not find the solution they need? Then, presumably the loosening of associations gets more and more pronounced ("reverse annealing") until it begins to interfere with the activities of daily living and thus begins to contribute net stress, thus making matters worse, not better. Now we have a pernicious positive feedback operating, and it rapidly worsens the state of the sufferer in what is known as a psychotic break, resulting in hospitalization. That these psychotic breaks are associated with tremendous stress is made clear by the fact that post-traumatic stress disorder is a common sequel of a psychotic episode.
Stress: Molecular aspects
01-06-2020: Messenger substances (i.e., hormones and neuromodulators) known to carry the stress signal are: CRF, ACTH, cortisol, noradrenaline, adrenaline, dopamine, NGF, and prolactin. The well-known phenomenon of stress sensitization, <05-31-2020: which may be part of the disease mechanism of schizophrenia,> probably inheres in long-term changes in protein expression and will not be apparent in a simple blood test for any of the above substances without a prior standardized stress challenge. (Could that be the process of getting the needle itself? In that case, you would install a catheter through the needle to permit repeated blood sampling and collect the baseline sample long after the intervention sample, not before, as is customary in research.)
Other mental illnesses
05-31-2020: Bipolar disorder may result from an analogous positive feedback affecting another problem solving adaptation of the brain, which would be modelled by the alternation of brainstorming sessions (mania) with sessions in which the brainstormed productions are soberly critiqued (depression).
Brain mechanisms
12-04-2020: How does the loosening of associations of schizophrenia arise? I conjecture that one activated sensory memory represented in the posterior cortex does not activate another directly, but indirectly via an anatomically lengthy but fast relay through the prefrontal cortex, which has a well known dopaminergic input from the ventral tegmental area of the midbrain. Imagine that a higher vertebrate has a free-will spectrum, with machine-like performance and high dopaminergic tone at one end, and at the other, a carefully considered performance verging on overthinking, with low dopaminergic tone. Persons with schizophrenia have presumably pushed past the latter end of the spectrum into dysfunction. Dopamine could orchestrate movement along the free-will spectrum by a dual action on the prefrontal cortex: inhibiting associational reflexes passing back to posterior cortex while facilitating direct outputs to the motor system. Dual actions of neuromodulators are a neuroscientific commonplace (e.g., my PhD thesis) and dopamine is a neuromodulator. It remains to be explained how the NMDA receptor, which is also strongly implicated in schizophrenia, enters the picture. <03-07-2021: It could simply be the source of excitation of the ventral tegmental area.>