c. 1600, "of or pertaining to natural science" (a sense now obsolete), from physiology + -ical. From 1814 as "of or pertaining to physiology, relating to the functions and properties of living bodies." Related: Physiologically.
1560s, "study and description of natural objects, natural philosophy" (a sense now obsolete), from French physiologie (16c.) or directly from Latin physiologia "natural science, study of nature," from Greek physiologia "natural science, inquiry into nature," from physios "nature" (see physio-) + logia "study" (see -logy). Meaning "science of the normal function of living things" is attested from 1610s. Related: Physiologic; physiologist.
The two words [physics/physiology] had once the same wide meaning of natural science or natural philosophy. They have now been narrowed & differentiated, physics retaining only the properties of matter & energy in inorganic nature, & physiology only the normal functions & phenomena of living beings. [Fowler, 1926]
compound adjectival word-forming element, usually interchangeable with -ic but sometimes with specialized sense (such as historic/historical, politic/political), Middle English, from Late Latin -icalis, from Latin -icus + -alis (see -al (1)). Probably it was needed because the forms in -ic often took on a noun sense (for example physic). Forms in -ical tend to be attested earlier in English than their twins in -ic.
<a href="https://www.etymonline.com/word/physiological">Etymology of physiological by etymonline</a>
Harper, D. (n.d.). Etymology of physiological. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/physiological