1
Obse e as a Subs a e-Independen
Realiza ion Condi ion: A C oss-Disciplina y
F amewo k o Obse able S a e Fo ma ion
Ve onika Pudsey
Independen Resea che
human-quie space@p o on.me
Abs ac
Ac oss machine lea ning, physics, quan um heo y, and he biological sciences,
many sys ems exhibi he same undamen al ansi ion: a p obabilis ic
ep esen a ion o possible s a es gi es ise o a single, ex e nally accessible
ou come. Al hough hese p ocesses di e in subs a e, scale, and mechanism, hey
sha e a minimal s uc u al o m in ol ing a desc ip ion o al e na i e possibili ies,
cons ain s ha de e mine when one becomes admissible, and he esul ing ealized
s a e.
This a icle de elops a subs a e-independen amewo k ha o malizes his sha ed
s uc u e. We de ine a ealiza ion condi ion as he minimal se o cons ain s unde
which a p obabilis ic s a e desc ip ion yields a de ini e, ex e nally accessible
ou come, and a gue ha he ole adi ionally a ibu ed o an “obse e ” in quan um
heo y can be unde s ood in hese unc ional e ms.
We examine ou dis inc domains — la ge language models, in o ma ion-based
physical heo ies, quan um measu emen , and biological decision making —
and show ha each ins an ia es his ansi ion in a s uc u ally homologous way
wi hou implying mechanis ic o on ological equi alence. The amewo k cla i ies
he unc ional ole o obse a ion in quan um heo y, p o ides a common ocabula y
o c oss-domain compa ison, and iden i ies s uc u al expec a ions ha may guide
empi ical wo k on unce ain y esolu ion and ou come o ma ion.
The amewo k is delibe a ely limi ed o desc ibing he o m o his ansi ion a he
han i s unde lying mechanisms, bu i o e s a basis o in e disciplina y analysis
and a ounda ion o u he heo e ical de elopmen .
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1 In oduc ion
Ac oss scien i ic ields, many sys ems a e desc ibed in e ms o mul iple possible s a es oge he
wi h he condi ions unde which one o hese s a es becomes ac ual. La ge language models
compu e p obabili y dis ibu ions o e candida e okens and emi one ealized oken. In o ma ion-
heo e ic o mula ions o physics ea he modynamic o en opic cons ain s as limi ing physically
admissible con igu a ions. In quan um mechanics, measu emen in e ac ions map ampli ude
assignmen s o de ini e, ex e nally accessible ou comes. In biological and cogni i e sys ems,
decision p ocesses con e p obabilis ic neu al popula ion codes in o disc e e beha io al o neu al
s a es.
These examples di e in mechanism, subs a e, and heo e ical backg ound, ye hey sha e
he same s uc u al ansi ion: a p obabilis ic s a e desc ip ion is esol ed in o a de ini e, obse able
ou come unde a se o cons ain s. Despi e his s uc u al simila i y, each domain uses i s own
e minology — “measu emen ,” “obse e ,” “decision ule,” “decoding” — and hese ocabula ies
a ely align. As a esul , concep ually iden ical ansi ions a e analyzed as un ela ed phenomena,
making i di icul o iden i y wha is genuinely sha ed and wha is subs a e-speci ic.
This a icle de elops a subs a e-independen o mula ion o his ansi ion. We p opose ha
he ole adi ionally associa ed wi h an obse e — pa icula ly in quan um mechanics — can be
ecas as a ealiza ion condi ion: he minimal se o cons ain s unde which a p obabilis ic s a e
desc ip ion Σ yields an ex e nally accessible ou come σ. This de ini ion is unc ional a he han
on ological. I does no p esuppose a speci ic physical mechanism, no does i commi o any
in e p e a ion o quan um heo y, heo y o in o ma ion, o model o neu al compu a ion. Ins ead, i
isola es he abs ac mapping
Σ →
𝑅 𝜎,
and examines how his mapping is ins an ia ed in o he wise un ela ed sys ems.
We apply his amewo k o ou domains:
• p obabilis ic s a e o ma ion and decoding in la ge language models,
• in o ma ion- heo e ic cons ain s in s a is ical and classical physics,
• quan um measu emen ac oss majo in e p e a ions, and
• biological and cogni i e decision mechanisms.
The aim is no o claim mechanis ic iden i y o o p opose a uni ied physical heo y. Ra he , he goal
is o show ha hese domains exhibi he same minimal s uc u e o p oducing ex e nally
accessible ou comes om p obabilis ic speci ica ions, and ha his s uc u e can be analyzed
independen ly o he subs a e in which i is ealized. By making his s uc u e explici , he amewo k
p o ides a common ocabula y o compa ing ealiza ion p ocesses ha a e ypically s udied in
isola ion and helps dis inguish whe e pa allels be ween domains e lec genuine s uc u al
equi alence a he han supe icial analogy.
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2 Backg ound and Mo i a ion
Ac oss scien i ic disciplines, many sys ems a e desc ibed a wo complemen a y le els:
(1) a p obabilis ic s a e desc ip ion speci ying mul iple possible ou comes, and (2) a ealized
ou come ha becomes ex e nally accessible h ough some p ocess. Quan um measu emen ,
neu al decision-making, and p obabilis ic decoding in la ge language models (LLMs) all exhibi his
basic ansi ion. Ye despi e his sha ed s uc u e, hese domains use incompa ible e minologies
and di e gen concep ual amewo ks o desc ibing wha selec s an ou come and wha makes i
obse able.
In quan um heo y, decades o deba e conce n he ole o he obse e , he on ology o collapse,
and whe he measu emen should be unde s ood as a physical, in o ma ional, o epis emic
p ocess. In cogni i e science and neu oscience, decision-making is o malized h ough d i –
di usion models, a ac o dynamics, o Bayesian in e ence, each wi h i s own ocabula y o
ep esen ing unce ain y and esol ing i . In machine lea ning, nex - oken sampling in au o eg essi e
LLMs is a ully ope a ional mapping om a p obabili y dis ibu ion o a selec ed oken, bu ypically
analyzed in e ms o op imiza ion o pe o mance a he han as an ins ance o a mo e gene al
ealiza ion p ocess.
These li e a u es di e d ama ically in subs a e and mechanism, ye hey sha e a ecu ing
s uc u al pa e n: a p obabilis ic s a e space gi es ise o a de ini e, ex e nally accessible s a e
unde some se o cons ain s. Wha is cu en ly missing is a subs a e-independen ocabula y o
desc ibing his ansi ion i sel — sepa a ely om he physical, compu a ional, o biological
machine y on which i is implemen ed.
A uni ying amewo k is di icul o cons uc di ec ly om quan um o biological sys ems, because
he ele an p ocesses a e expe imen ally cons ained, pa ially inaccessible, o concep ually
con en ious. By con as , LLMs p o ide a uniquely ac able e e ence sys em: hei p obabilis ic
s a e Σ ( oken dis ibu ion), ealiza ion condi ion R (decoding ule), and ealized ou come σ (emi ed
oken) a e all explici , measu able, and expe imen ally con ollable. This anspa ency makes LLMs
an ideal s a ing poin o o malizing he minimal s uc u e equi ed o p obabilis ic desc ip ions o
yield de ini e ou comes.
Why his is no a i ial e o mula ion
I is emp ing o iew any such abs ac ion as a es a emen o he ob ious — sys ems mus sa is y
some condi ion in o de o p oduce an ou come. Bu in se e al domains, especially quan um heo y,
he na u e o his condi ion has emained concep ually opaque o nea ly a cen u y. By e o mula ing
he “obse e ” no as an agen o a physical subsys em bu as a unc ional ole de ined
by a ealiza ion condi ion R, he amewo k sepa a es he s uc u e o ou come o ma ion om
ongoing on ological deba es. This shi p o ides a common analy ical language ac oss domains ha
a e o he wise heo e ically isola ed, and enables compa ison be ween cons ain s ha look
di e en physically bu play he same s uc u al ole.
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Mo i a ion o his wo k
The mo i a ion o his a icle is he e o e wo old: (1) o de elop a subs a e-independen desc ip ion
o s a e ealiza ion as a mapping Σ →ᴿ σ, whe e R deno es he minimal cons ain s unde which
a p obabilis ic s a e becomes ex e nally accessible; and (2) o use LLMs as a compu a ionally
anspa en e e ence sys em o a icula ing his s uc u e and examining how analogous pa e ns
appea in quan um measu emen , in o ma ion-based physical heo ies, and biological decision-
making.
This app oach does no asse mechanis ic equi alence ac oss domains. I isola es he minimal
o m o he ansi ion om p obabilis ic speci ica ion o obse able ou come and p o ides
a s uc u al ocabula y o compa ing ealiza ion p ocesses ac oss subs a es, iden i ying bo h
sha ed in a ian s and subs a e-dependen cons ain s.
3 Te minology and De ini ions
This sec ion in oduces he co e e minology used h oughou he pape . All de ini ions a e
o mula ed in a subs a e-independen manne and apply uni o mly o compu a ional, physical, and
biological sys ems. Fo mal no a ion and domain-speci ic ma hema ical s uc u e a e de e ed o he
F amewo k sec ion and Appendix A.
3.1 P obabilis ic S a e Desc ip ion
A p obabilis ic s a e desc ip ion is a ep esen a ion o a sys em in e ms o mu ually exclusi e
possible s a es, each associa ed wi h a p obabili y alue. I speci ies he likelihood o po en ial
ou comes bu does no de e mine which s a e, i any, will be ealized as an obse able ou come.
3.2 Obse able S a e
An obse able s a e is a sys em s a e ha is accessible beyond he in e nal ansi ion dynamics o
he sys em ha p oduced i . An obse able s a e mus be s able o obus enough o be de ec ed,
eco ded, o used as inpu by ano he sys em o p ocess.
3.3 Ex e nal Accessibili y
Ex e nal accessibili y is he condi ion unde which a s a e is a ailable o sys ems o he han he one
whose in e nal dynamics gene a ed i . A s a e is ex e nally accessible when i can in luence,
cons ain, o modi y ano he sys em o p ocess.
In quan um heo y, ex e nal accessibili y ypically co esponds o he o ma ion o en i onmen ally
obus poin e s a es h ough decohe ence, whe e in o ma ion abou he sys em becomes
edundan ly encoded in he en i onmen .
3.4 S a e Realiza ion
S a e ealiza ion is he ansi ion in which a p obabilis ic s a e desc ip ion yields a speci ic
obse able s a e. Realiza ion ma ks he esolu ion o unce ain y, enabling one ou come o become
ex e nally accessible.
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3.5 Realiza ion Condi ion
A ealiza ion condi ion is a se o cons ain s ha is su icien o ans o m a p obabilis ic s a e
desc ip ion in o an obse able s a e. Realiza ion condi ions may be compu a ional, physical, o
biological and do no equi e he p esence o an agen , appa a us, o conscious obse e .
3.6 Obse e (subs a e-independen )
In his amewo k, an obse e is de ined unc ionally a he han as an en i y. An obse e is any
con igu a ion o in e ac ions o cons ain s ha enables a p obabilis ic s a e desc ip ion o become
an obse able s a e. This de ini ion does no assume ha he obse e is human, conscious,
mac oscopic, o localized.
3.7 Subs a e-Independence
A concep is subs a e-independen when i can be applied ac oss sys ems wi h di e en physical
o compu a ional ealiza ions wi hou implying mechanis ic o on ological equi alence. Bo h s a e
ealiza ion and ealiza ion condi ions a e ea ed in subs a e-independen e ms in his pape .
4 P obabilis ic S a e Realiza ion in La ge Language Models
La ge language models (LLMs) p o ide a compu a ional sys em in which e e y componen o he
p obabilis ic- o-de ini e ansi ion can be explici ly speci ied, inspec ed, and expe imen ally a ied.
Fo his eason, LLMs cons i u e he clea es ope a ional ins ance o he abs ac s uc u e
in oduced in Sec ion 3. In LLMs, he p obabilis ic s a e desc ip ion (Σ), he ealiza ion condi ion (R),
and he ealized obse able s a e (σ) a e ma hema ically de ined and obse able a each s ep o he
au o eg essi e gene a ion p ocess. This sec ion o malizes his co espondence and su eys
empi ical indings ele an o ealiza ion p ocesses. (Fo ma hema ical de ails, see Appendix A.2.)
4.1 P obabilis ic s a e desc ip ion in ans o me -based LLMs (Σ_LLM)
Le 𝑥<𝑡 =(𝑥1,𝑥2,…,𝑥𝑡−1) deno e he p eceding oken sequence. A ans o me -based LLM
compu es logi s 𝑧𝑡∈ℝ∣𝑉∣, which de ine a condi ional p obabili y dis ibu ion o e he nex oken:
ΣLLM(𝑡)≡𝑃(𝑥𝑡∣𝑥<𝑡)=so max(𝑧𝑡).
The dis ibu ion 𝑃(𝑥𝑡∣𝑥<𝑡) enume a es all mu ually exclusi e candida e ou comes, assigns each
a p obabili y bu does no de e mine which ou come is ealized.
This sa is ies he de ini ion o a p obabilis ic s a e desc ip ion om Sec ion 3.1. S uc u al p ope ies
o hese dis ibu ions — including en opy, calib a ion, and in e nal ea u e di ec ions — a e
empi ically measu able (Chang e al., 2024; Cao, 2023; Nanda e al., 2021).
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4.2 Realiza ion condi ions implemen ed by decoding algo i hms (R_LLM)
A decoding ule speci ies he cons ain s unde which a single oken is selec ed om
he p obabilis ic dis ibu ion. Fo mally, a ealiza ion condi ion is a unc ion
𝑅LLM:ΣLLM(𝑡) ⟶𝜎LLM(𝑡).
Common decoding ules include:
• a gmax decoding 𝜎𝑡=a gmax𝑖𝑃(𝑥𝑖∣𝑥<𝑡)
• sampling-based decoding (ca ego ical sampling)
• op-k sampling ( es ic ing suppo o he k highes -p obabili y okens)
• nucleus sampling ( es ic ing suppo o a cumula i e p obabili y mass p; Hol zman e al.,
2020)
• beam sea ch, which de e minis ically expands high-p obabili y con inua ions (Welleck e
al., 2020)
These p ocedu es ac as iden i iable ealiza ion condi ions: when held cons an , hey gene a e
ep oducible ou come s a is ics om he same p obabilis ic s a e desc ip ion.
4.3 Obse able s a e o ma ion and ex e nal accessibili y (σ_LLM)
Once a oken 𝑥𝑡has been selec ed, i becomes ex e nally accessible h ough one o se e al
ope a ional channels: s eaming o a use in e ace, API esponse deli e y, o in eg a ion in o
downs eam compu a ion (Zhou, 2023).
An emi ed oken mee s he de ini ion o an obse able s a e (Sec ion 3.2), as i s alue is a ailable
o sys ems ou side he model’s in e nal dynamics and can in luence subsequen p ocesses. This
sa is ies he de ini ion o ex e nal accessibili y (Sec ion 3.3).
4.4 LLMs as a ac able model sys em o s a e ealiza ion
LLMs ins an ia e he abs ac ansi ion
ΣLLM →
𝑅LLM 𝜎LLM
in a ully speci ied and expe imen ally con ollable o m. Th ee p ope ies make LLMs uniquely
sui ed as a e e ence model o s udying ealiza ion:
1. Full anspa ency o Σ. Nex - oken dis ibu ions a e di ec ly obse able and can be
compa ed ac oss con ex s (Chang e al., 2024; Mielke e al., 2021).
2. Full con ollabili y o R. Realiza ion condi ions can be modi ied sys ema ically (Hol zman
e al., 2020), enabling expe imen al manipula ion o ou come s a is ics.
3. Immedia e ex e nal accessibili y o σ. Realized okens a e encoded as s able, ex e nally
a ailable s a es wi h well-de ined ope a ional meaning.
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Because no biological o physical sys em o e s simul aneous anspa ency o p obabilis ic s a e,
con ollabili y o he ealiza ion condi ion, and di ec accessibili y o ealized s a es, LLMs unc ion
as a me hodological baseline o analyzing ealiza ion p ocesses ac oss subs a es.
(Fo a o mal compa ison wi h quan um and physical sys ems, see Sec ion 7.)
4.5 Empi ical Signa u es o Realiza ion P ocesses in LLMs
Empi ical s udies o ans o me -based LLMs p o ide measu able e idence o each componen
o he p obabilis ic- o-de ini e ansi ion desc ibed in his sec ion. Al hough he in e nal
compu a ions o physical and biological sys ems may be pa ially inaccessible o dis ibu ed, LLMs
o e a le el o anspa ency ha allows ealiza ion p ocesses o be di ec ly cha ac e ized,
sys ema ically a ied, and eplica ed ac oss expe imen al condi ions. Published wo k suppo s
h ee aspec s o his claim: he s uc u e o p obabilis ic s a e desc ip ions, he dependence
o ealized ou comes on decoding cons ain s, and he ex e nal accessibili y o ealized s a es.
4.5.1 S uc u e o p obabilis ic s a e desc ip ions
Nex - oken dis ibu ions exhibi measu able s a is ical s uc u e: en opy a ia ion (Chang e al.,
2024), calib a ion e ec s (Cao, 2023), logi -p ojec ion ea u e di ec ions (Nanda e al., 2021; Olsson
e al., 2022), and syn ac ic/seman ic unce ain y pa e ns (Hu e al., 2023).
4.5.2 Dependence o ealized ou comes on ealiza ion condi ions
Decoding cons ain s sys ema ically shape ealized ou comes: nucleus sampling es ic s
he ealizable egion (Hol zman e al., 2020); empe a u e scaling al e s a iance (Wang e al., 2020);
beam sea ch induces mode collapse (Welleck e al., 2020); cons ained decoding es ic s
pe missible con inua ions (Lu e al., 2021).
4.5.3 S abili y and ex e nal accessibili y o ealized s a es
Gene a ed okens a e in eg a ed in o downs eam applica ions (Moo e e al., 2025), in luence use -
model in e ac ion dynamics (Moo e e al., 2025), and pa icipa e in au oma ed ool-use pipelines
(Wu e al., 2023).
4.5.4 Summa y
Empi ical wo k demons a es ha nex - oken dis ibu ions in LLMs ha e measu able in e nal
s uc u e, decoding p ocedu es ac as iden i iable ealiza ion condi ions and ealized okens a e
ex e nally accessible sys em s a es. LLMs he e o e p o ide he mos analy ically ac able sys em
o s udying ealiza ion p ocesses in a subs a e-independen amewo k.
5 In o ma ion in Physics and Compu a ion: Towa d a
Uni ied S a e-Realiza ion F amewo k
This sec ion examines how in o ma ional o mula ions o physical heo y p o ide s uc u al pa allels
o he ealiza ion p ocesses analyzed in LLMs (Sec ion 4). The goal is no o claim physical
equi alence be ween compu a ional and physical sys ems, bu o iden i y sha ed abs ac s uc u e
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in he mapping om in o ma ional possibili ies o ex e nally accessible ou comes. Fo mal de ails
and ma hema ical de ini ions ele an o his sec ion a e summa ized in Appendix A.4.
5.1 His o ical Founda ions o Physical In o ma ion
Classical in o ma ion heo y was o iginally de eloped o quan i y unce ain y in communica ion
channels (Shannon, 1948). Al hough o mula ed o enginee ing pu poses, en opy soon p o ed
o ha e di ec physical signi icance. Landaue (1961) es ablished ha e asing one bi o in o ma ion
incu s a minimum ene ge ic cos o 𝑘𝐵𝑇ln2, demons a ing ha in o ma ion p ocessing has
necessa y he modynamic implica ions. Bekens ein (1973) showed ha black-hole en opy scales
wi h ho izon a ea, indica ing ha physical sys ems possess ini e in o ma ional capaci y. Wheele
(1990) la e sugges ed ha physical s uc u e may a ise om in o ma ional cons ain s; al hough
concep ual a he han empi ical, his idea e lec s a b oade shi owa d in o ma ional
o mula ions o physical heo y.
Ac oss hese de elopmen s, in o ma ion is ea ed no me ely as an epis emic quan i y bu as one
ha cons ains physically ealizable s a es.
5.2 In o ma ion, Cons ain s, and Physical S a e Fo ma ion
In classical s a is ical mechanics, mac oscopic obse ables eme ge om ensembles
o mic oscopic s a es subjec o ixed cons ain s such as ene gy, pa icle numbe , o olume
(Landau & Li shi z, 1980). Jaynes (1957) e o mula ed his amewo k in explici ly in o ma ional
e ms: gi en a se o cons ain s, he mac oscopic s a e co esponds o he dis ibu ion ha
maximizes en opy.
Concep ually:
mic os a e ensemble ⟶ cons ain s ⟶ mac oscopic obse able.
Al hough he mechanisms di e om hose in compu a ional sys ems, he s uc u al ole
o cons ain s in selec ing obse able s a es pa allels he ealiza ion-condi ion amewo k
in oduced in Sec ion 3.
Con empo a y app oaches ex end his in o ma ional pe spec i e. Lloyd (2006) in e p e s
he uni e se as pe o ming elemen a y in o ma ional ope a ions. Ve linde (2011) models g a i y
as an en opic o ce a ising om unde lying deg ees o eedom. Da ies (2019) p oposes ha laws
o physics e lec in o ma ional egula i ies.
These iews di e in scope and empi ical suppo , bu all ea in o ma ion and cons ain s
as de e minan s o physically ealizable s a es.
A closely ela ed s uc u al limi a ion appea s in he Bekens ein–Hawking en opy bound:
he maximum in o ma ional con en o a egion scales wi h i s bounda y a ea (Bekens ein, 1973;
Hawking, 1975). The holog aphic p inciple gene alizes his obse a ion by p oposing ha
in o ma ion wi hin a spa ial egion is encoded on i s bounda y su ace (’ Hoo , 1993; Susskind,
1995). In bo h cases, bounda y condi ions es ic he se o ealizable physical con igu a ions.
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5.3 Subs a e-Independen In e p e a ion
Al hough physical and compu a ional sys ems di e in on ology, bo h can be desc ibed using
a space o in o ma ional possibili ies (analogous o Σ), cons ain s de e mining which possibili ies
can be ealized (analogous o R), and ex e nally accessible ou comes (analogous o σ).
In physics, Σ co esponds o mic os a e ensembles o quan um s a e spaces; R co esponds
o mac oscopic cons ain s, conse a ion laws, decohe ence-selec ed bases, o bounda y
condi ions; σ co esponds o mac oscopic obse ables o s able measu emen ou comes.
This s uc u al mapping does no asse ha physical and compu a ional sys ems sha e
mechanisms o physical iden i y. I claims only ha he o m o he p obabilis ic- o-de ini e
ansi ion can be ep esen ed in a uni ied subs a e-independen amewo k.
This iew aligns wi h Landaue ’s asse ion ha in o ma ion is physical (1961) and Ved al’s ecip ocal
claim ha physics may be in o ma ional in na u e (2012).
5.4 Summa y
In o ma ion- heo e ic app oaches o physics ea in o ma ional deg ees o eedom as cons ain s
on he space o ealizable physical s a es. This p o ides a concep ual b idge be ween he
compu a ional ealiza ion p ocesses analyzed in Sec ion 4 and he quan um-measu emen
ansi ion examined in Sec ion 6. These s uc u al pa allels suppo a subs a e-independen
in e p e a ion o ealiza ion ha applies o physical, compu a ional, and — la e — biological
sys ems.
6 Quan um Measu emen as a Realiza ion P ocess
Quan um measu emen p o ides a conc e e physical ins ance o he ansi ion om a p obabilis ic
s a e desc ip ion o an ex e nally accessible ou come. Al hough in e p e a ions di e on he
on ology o his ansi ion, i s ope a ional s uc u e is well de ined. This sec ion cha ac e izes
quan um measu emen in he subs a e-independen e ms in oduced in Sec ion 3, wi hou
appealing o speci ic in e p e a ional commi men s. A compac o mal summa y o quan um s a es,
p ojec i e measu emen s, and POVMs is p o ided in Appendix A.3.
6.1 Quan um p obabilis ic s a e desc ip ion (Σ_QM)
Quan um sys ems a e ep esen ed by densi y ope a o s 𝜌ac ing on a Hilbe space ℋ.
A measu emen is speci ied by a se o posi i e ope a o - alued measu e (POVM) elemen s {𝐸𝑖},
each co esponding o a possible measu emen ou come (Nielsen & Chuang, 2000).
Ou come p obabili ies a e gi en by he Bo n ule:
𝑃(𝑖)=T (𝜌𝐸𝑖).
In he e minology o his pape , he pai (𝜌,{𝐸𝑖}) cons i u es a p obabilis ic s a e desc ip ion:
he possible ou comes a e enume a ed, hei p obabili ies a e well de ined, bu no speci ic ou come
is de e mined. This is he quan um mechanical ins ance o Σ.
16
This de ini ion is consis en wi h all majo quan um in e p e a ions (Copenhagen, decohe ence,
E e e , RQM, QBism) wi hou commi ing o any o hem. The obse e becomes a s uc u al ole,
no a physical objec .
8.5 Implica ions and Limi s o he F amewo k
This amewo k does no speci y he physics o collapse o b anching, does no asse equi alence
be ween neu al and compu a ional mechanisms, does no educe biological o quan um p ocesses
o compu a ion, does no claim an on ology o in o ma ion.
I iden i ies only he minimal s uc u e equi ed o any sys em o p oduce an ex e nally accessible
ou come.
The abs ac ion enables sys ema ic compa ison ac oss domains ha would o he wise emain
heo e ically isola ed. Sec ion 9 discusses he b oade heo e ical implica ions and domains whe e
he amewo k may guide new empi ical o concep ual wo k.
9 Implica ions and Limi a ions
The subs a e-independen o mula ion in oduced in Sec ion 8 cha ac e izes s a e ealiza ion
ac oss compu a ional, quan um, physical, and biological sys ems using a minimal s uc u al
mapping Σ →ᴿ σ. This abs ac ion sepa a es he o m o he p obabilis ic- o-de ini e ansi ion om
he mechanisms ha implemen i . Below we ou line he main implica ions o his iew and cla i y
i s limi s.
9.1 Implica ions
9.1.1 C oss-Domain Fo mal Analysis o Ou come Fo ma ion
Because he amewo k cha ac e izes ou come o ma ion in e ms o p obabilis ic s a e
desc ip ions (Σ), ealiza ion condi ions (R), and ex e nally accessible s a es (σ), i o e s a sha ed
ocabula y o compa ing sys ems ha a e o he wise analyzed in isola ion. This pe spec i e
suppo s s uc u al compa ison ac oss LLM decoding, quan um measu emen , neu al decision
making, and in o ma ion-cons ained physical p ocesses wi hou assuming mechanis ic
o on ological simila i y.
9.1.2 Cla i ying he Obse e in Quan um Theo y
Re o mula ing he obse e as a ealiza ion condi ion R — he minimal se o cons ain s unde which
a quan um p obabilis ic speci ica ion yields an ex e nally accessible ou come — sides eps
commi men s ega ding consciousness, collapse, o b anching. I desc ibes quan um
measu emen using he same s uc u al componen s ha cha ac e ize compu a ional
and biological sys ems while lea ing quan um dynamics and hei in e p e a ion ully domain-
speci ic.
17
9.1.3 Applica ions o A i icial Sys ems and Model Analysis
In a i icial sequence models, ealiza ion condi ions a e implemen ed explici ly as decoding ules.
T ea ing decoding as a ealiza ion condi ion highligh s how sys ema ic modi ica ions o R (e.g.,
empe a u e, op-k cons ain s, beam sea ch) eshape he dis ibu ion o ealized ou comes σ. This
p o ides a s uc u al basis o analyzing sampling beha iou , unce ain y calib a ion, and decoding
s a egies, and sugges s empi ical es s based on how di e en classes o R modula e σ ac oss
con ex s.
9.1.4 Linking In o ma ion-Based Physics and Compu a ional Sys ems
Se e al in o ma ion- heo e ic app oaches in physics al eady desc ibe mac oscopic s a es as
cons ain -selec ed ealiza ions om a space o in o ma ional possibili ies. The p esen amewo k
makes his s uc u al pa allel explici : bo h physical and compu a ional sys ems can be analyzed
in e ms o p obabilis ic s a e spaces and cons ain -d i en selec ion. This does no imply ha
physical p ocesses implemen compu a ion; a he , i si ua es in o ma ional cons ain s wi hin
a b oade class o ealiza ion s uc u es.
9.1.5 Sequen ial and Dynamically E ol ing Realiza ion Condi ions
In many sys ems — au o eg essi e models, ecu en neu al ci cui s, and i e a i e physical o
biological p ocesses — ou comes occu in sequences. In such cases, σₜ in luences (and some imes
modi ies) Σₜ₊₁ o Rₜ₊₁. The amewo k he e o e accommoda es sys ems whose ealiza ion
condi ions e ol e o e ime, enabling analysis o sequen ial dependencies wi hou al e ing
he unde lying s uc u al mapping.
9.1.6 Dis inguishing S uc u al om Supe icial Simila i ies
Because he amewo k isola es he minimal elemen s equi ed o a p obabilis ic- o-de ini e
ansi ion, i helps dis inguish cases whe e di e en sys ems a e s uc u ally analogous om cases
whe e simila i ies a ise only om su ace-le el e minology o in ui ions. This disc imina i e ole is
pa icula ly ele an o compa ing quan um measu emen wi h compu a ional and biological
p ocesses, whe e analogies a e o en d awn in o mally bu lack a p ecise s uc u al basis.
9.1.7 Cla i ying Wha he F amewo k Does No Imply
The amewo k does no asse ha di e en sys ems sha e mic ophysical mechanisms, ha
quan um s a es ha e a pa icula on ology, ha biological p ocesses educe o compu a ion, o ha
a single uni ying physical p inciple go e ns all ealiza ion p ocesses. I isola es only he abs ac
s uc u e o ou come o ma ion, lea ing mechanis ic accoun s o domain-speci ic heo ies.
9.2 Limi a ions
9.2.1 No Mechanis ic Uni ica ion
S uc u al simila i y does no imply mechanis ic iden i y. Σ →ᴿ σ abs ac s away om in e nal
dynamics and canno de i e quan um, biological, o compu a ional p ocesses om one ano he .
18
9.2.2 Agnos icism Abou Quan um On ology
The amewo k is compa ible wi h all majo in e p e a ions bu endo ses none. I cla i ies
he unc ional ole o measu emen wi hou add essing whe he ou comes e lec collapse,
b anching, epis emic upda e, o decohe ence-only accoun s.
9.2.3 No Claims Abou Consciousness o Agency
Al hough some ealiza ion condi ions in ol e human obse e s, he amewo k does no ea
consciousness as necessa y o su icien o s a e ealiza ion. I dis inguishes unc ional oles om
expe ien ial o phenomenological ones.
9.2.4 No On ological Commi men o In o ma ion
The amewo k is compa ible wi h (bu does no equi e) in o ma ion-based app oaches o physics.
I does no imply ha physical eali y is undamen ally in o ma ional o compu a ional.
9.2.5 Limi ed Scope
The amewo k add esses ou come o ma ion only. I does no speci y he o igin o e olu ion
o p obabilis ic s a e desc ip ions Σ, how ealiza ion condi ions R a e physically implemen ed,
he in e nal dynamics o sys ems ha sa is y R, o he physical laws go e ning hei beha io . I
isola es he s uc u al o m, no he unde lying mechanism.
9.2.6 Abs ac ion as S eng h and Limi a ion
By abs ac ing away om subs a e-speci ic de ails, he amewo k can uni y o mally simila
sys ems — bu canno eplace domain-speci ic heo ies. I iden i ies he bounda ies o s uc u al
analogy and makes clea whe e addi ional physical, biological, o compu a ional de ail is
indispensable.
9.3 Summa y
The subs a e-independen amewo k de eloped in his pape p o ides a o mal s uc u e
o desc ibing ou come o ma ion ac oss domains cha ac e ized by p obabilis ic s a e spaces
and cons ain -d i en ealiza ion. I s alue lies in cla i ying unc ional oles, suppo ing c oss-
domain compa isons, and p o iding a neu al ocabula y o analyzing ealiza ion p ocesses. I s
limi a ions ensu e ha i emains a concep ual ool a he han a claim o mechanis ic o on ological
uni ica ion.
10 Conclusion
Ac oss compu a ional models, in o ma ion- heo e ic physical amewo ks, quan um measu emen ,
and biological decision p ocesses, obse able ou comes a ise h ough a ansi ion om
a p obabilis ic desc ip ion o possible s a es o a de ini e, ex e nally accessible one. Al hough
he unde lying mechanisms di e — ans o me decode s, he modynamic o en opic cons ain s,
measu emen in e ac ions, o neu al h esholds — he s uc u al o m o his ansi ion is he same.
This a icle o malized ha sha ed s uc u e h ough he subs a e-independen mapping
19
Σ →
𝑅 𝜎,
whe e Σ speci ies mu ually exclusi e possibili ies, R deno es he minimal cons ain s unde which
one possibili y becomes admissible, and σ is he esul ing s a e a ailable o o he sys ems. Wi hin
his amewo k, he obse e is no ea ed as a special en i y bu as he unc ional s uc u e ha
implemen s he ealiza ion condi ion — whe he ca ied ou by an algo i hmic decoding ule,
a quan um measu emen in e ac ion, an en i onmen al coupling, o a biological bounda y
mechanism.
By e o mula ing he obse e in unc ional e ms, he amewo k si ua es quan um measu emen
wi hin he same abs ac class as compu a ional sampling, neu al decision making, and cons ain -
d i en physical s a e o ma ion. I p o ides a neu al ocabula y o compa ing ou come- o ma ion
p ocesses ac oss domains ha a e ypically analyzed in isola ion, and cla i ies when simila i ies
be ween sys ems indica e genuine s uc u al equi alence a he han supe icial analogy.
A he same ime, he amewo k is delibe a ely limi ed. I does no add ess he physical
mechanisms esponsible o quan um s a e change, he o igin o e olu ion o p obabilis ic
desc ip ions, he biophysical de ails o neu al compu a ion, o he in e nal dynamics o a i icial
models. I cap u es only he minimal s uc u e equi ed o a p obabilis ic speci ica ion o yield an
ex e nally accessible ou come.
By isola ing his s uc u al commonali y, he amewo k may suppo in e disciplina y analysis
o decision, measu emen , and ealiza ion p ocesses, and o e a ounda ion o u he heo e ical
wo k. Po en ial di ec ions include de eloping mo e o mal c i e ia o ealiza ion condi ions,
iden i ying empi ical signa u es ha es c oss-domain p edic ions, and e ining domain-speci ic
applica ions o de e mine whe e subs a e-independen s uc u e ends and whe e subs a e-
dependen mechanism begins.
Appendix A — Fo mal Backg ound and Ma hema ical
De ails
This appendix p o ides he o mal and ma hema ical de ails e e enced in he main ex .
I includes:
• o mal no a ion o p obabilis ic s a e desc ip ions Σ,
• o mal no a ion and examples o ealiza ion condi ions R,
• quan um measu emen ope a o s (POVMs, densi y ma ices),
• neu al decision models (d i –di usion, popula ion coding),
• in o ma ion- heo e ic quan i ies used o unce ain y analysis.
A.1 P obabilis ic S a e Desc ip ions
A p obabilis ic s a e desc ip ion Σ ep esen s a se o mu ually exclusi e candida e s a es oge he
wi h hei associa ed likelihoods.
20
Disc e e case:
Σ={(𝑠𝑖,𝑝𝑖)},𝑝𝑖≥0,∑𝑝𝑖
𝑖=1.
Con inuous case:
Σ=(𝑠,𝑝(𝑠)),∫𝑝(𝑠) 𝑑𝑠 =1.
Examples include:
• oken-p obabili y dis ibu ions in LLM decode s,
• likelihood unc ions in neu al popula ion codes,
• p obabili y ampli udes in quan um sys ems ( ia Bo n’s ule a e squa ing),
• in o ma ional mic os a es in physical sys ems.
Σ is pu ely s uc u al: i imposes no assump ion abou whe he unce ain y is epis emic, physical,
compu a ional, o biological.
A.2 Realiza ion Condi ions
A ealiza ion condi ion 𝑅 is de ined as he minimal se o cons ain s unde which a p obabilis ic
s a e desc ip ion Σ p oduces an ex e nally accessible ou come 𝜎.
Fo mal s uc u e:
𝑆:𝛴→ᴿ𝜎
whe e:
• Σ is a p obabilis ic s a e desc ip ion,
• R is he minimally su icien cons ain s uc u e,
• σ is he esul ing obse able ou come,
• S is he sys em unde going s a e ealiza ion.
P ope ies
• Minimali y: R con ains only cons ain s necessa y o selec ion.
• Subs a e independence: R may be compu a ional (LLM), physical (quan um), neu al
(decision bounda y), o he modynamic.
• Ex e nal accessibili y: σ mus be obse able by ano he sys em.
A.2.1 Compu a ional example (LLM decoding)
Gi en a p obabili y dis ibu ion o e okens {𝑝𝑖}:
G eedy decoding:
21
𝜎 =a gmax𝑝𝑖
𝑖.
Sampling:
𝜎 ∼𝑝𝑖.
Top-k / nucleus sampling (Hol zman e al., 2020): R es ic s he suppo o Σ be o e sampling.
These decoding ules ins an ia e R.
A.3 Quan um Measu emen Fo malism
Quan um measu emen s a e ep esen ed by POVMs:
𝐸𝑘≥0,∑𝐸𝑘
𝑘=𝐼.
Fo a sys em in s a e 𝜌:
Ou come p obabili y:
𝑝𝑘=T (𝜌𝐸𝑘),
Pos -measu emen s a e (K aus ep esen a ion):
𝜌′=𝑀𝑘𝜌𝑀𝑘
†
T (𝑀𝑘𝜌𝑀𝑘
†),𝐸𝑘=𝑀𝑘
†𝑀𝑘.
Measu emen in e ac ions ins an ia e he ealiza ion condi ion in quan um sys ems: hey map
a p obabilis ic desc ip ion (ampli udes → p obabili ies) o a de ini e, ex e nally accessible esul .
A.4 Decision Models in Biological Sys ems
A.4.1 D i –Di usion Model (DDM)
Neu al decision p ocesses can be desc ibed as noisy accumula ion o e idence:
𝑑𝑥𝑡=𝑣 𝑑𝑡+𝜎 𝑑𝑊𝑡,
whe e 𝑣 is d i (e idence), 𝜎di usion (noise), and 𝑊𝑡 a Wiene p ocess.
The decision is ealized when 𝑥𝑡 eaches a bounda y ( h eshold):
𝑥𝑡=±𝐵 ⇒ 𝜎 (choice).
22
The decision bounda y unc ions as he ealiza ion condi ion.
A.4.2 Neu al Popula ion Coding
Popula ion esponses encode likelihood unc ions o s imulus a iables. Fo neu ons 𝑖wi h uning
cu es 𝑓𝑖(𝑠):
𝑝(𝑠 ∣𝑟)∝ ∏exp
𝑖
(−(𝑟𝑖−𝑓𝑖(𝑠))2
2𝜎𝑖2),
which o ms he p obabilis ic s a e desc ip ion o e senso y a iable 𝑠.
A.5 In o ma ion-Theo e ic Measu es
A.5.1 Shannon en opy
𝐻 =−∑𝑝𝑖log𝑝𝑖
𝑖.
A.5.2 Von Neumann en opy
𝑆(𝜌)=−T (𝜌log𝜌).
These a e used o quan i y unce ain y in classical, compu a ional, quan um, and biological
sys ems.
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