Involuntary Arousal (Taḥarruk al-Sākin)1

Answer—and Allah is the Guide to success: The scholars of the madhhab said—as in al-Azhār—“For movement of what is dormant (taḥarruk al-sākin) a sheep [is due].” In the Sharḥ it adds: that is when it is stirred by desire through touching, kissing, or looking; he, peace be upon him, or by speech, or by deliberate reflection.
On this basis, nothing is due from the questioner so long as no cause for the arousal issued from him—namely touching, kissing, looking, or deliberate reflection.
I say: a muḥrim often finds his gaze falling upon women due to their abundance in those places, and he may be forced into jostling with them at some congested points. In such cases, if involuntary arousal occurs, nothing is due upon him—unless he persists in staring or in jostling while he is able to avoid it.
Moreover, Imām al-Hādī ilā al-Ḥaqq—peace be upon him—interpreted “the minor offenses (al-lammam)” in His saying, “Those who avoid the major sins and immoralities—except for the lesser [offense]. Indeed your Lord is vast in forgiveness.” [al-Najm:32] as akin to a man’s unintended pressing against a woman at the Kaʿbah.
And Allah Most High said, “And there is no blame upon you for that in which you have erred, but [only] for what your hearts intended.” [al-Aḥzāb:5]. Thus, when looking and jostling are not deliberate, there is no blame upon the muḥrim for that, nor for any involuntary arousal resulting from it. Allah Most High also said, “Allah does not charge a soul except [with that within] its capacity.” [al-Baqarah:286]
Likewise is the ruling on thoughts: if the muḥrim deliberately entertains erotic thoughts, then a sheep is due for the ensuing arousal. But if the thoughts were not intended—arising without his willing them—then nothing is due for the arousal; for Allah does not burden a soul beyond its capacity, and a person is not able to rid himself entirely of the mind’s whisperings. What is within his ability is to push the thoughts away: if he does not push them away but follows them and takes pleasure in the whisperings, then his ruling is that of the deliberate doer; but if he resists, nothing is upon him. All of this is indicated by the two verses cited.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.1