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Nega i e Hea Capaci y in Sel -G a i a ing Sys ems
Jae Un Kim
Depa men o Physics in Ajou Uni e si y
Cou se Ti le
P o esso Name
Oc obe 27, 2025
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Abs ac
Nega i e Hea Capaci y in Sel -G a i a ing Sys ems
The phenomenon o nega i e hea capaci y—whe e a sel -g a i a ing sys em becomes ho e as
i loses ene gy—can be aced h ough a sequence o mic oscopic p ocesses ha connec he mal
ene gy loss, densi y a ia ion, and collisional dynamics.
When ex e nal hea is eleased, he mean kine ic ene gy (K) dec eases and he a e age pa icle
eloci y ( ) diminishes. This educ ion in eloci y weakens he o e all dynamic p essu e and
causes pa icles o emain wi hin he same spa ial egion o a longe ime. As a esul , he local
pa icle densi y (ρ) inc eases—no solely due o g a i a ional con ac ion bu also because o
kinema ic s agna ion, whe e slowe pa icles accumula e simply by s aying longe in one place.
As he densi y ises, he g a i a ional po en ial ene gy (Ug) becomes mo e nega i e, indica ing a
deepe g a i a ional well and s onge con inemen . Simul aneously, he numbe o pa icles pe
uni olume inc eases, which aises he collision p obabili y (Pcoll) e en i pa icle eloci ies a e
educed. This means ha collisions occu mo e equen ly no only because he po en ial well
deepens, bu also because he e a e physically mo e pa icles wi hin he same egion.
The enhanced collision equency inc eases he a e o ene gy edis ibu ion among pa icles,
leading o a pa ial eco e y o in e nal ene gy (U). Consequen ly, he a e age kine ic empe a u e
(T) ises e en hough he o al ene gy (E=K+Ug) con inues o dec ease. The p ocess he e o e
yields a he mal in e sion cha ac e is ic o sel -g a i a ing sys ems, exp essed as C=dE/dT <0.
The o e all sequence p oceeds as ollows:
1. Ex e nal hea loss →Dec ease in kine ic ene gy and pa icle eloci y
2. Reduced eloci y →Longe esidence ime →Local densi y inc ease
3. Densi y inc ease →G a i a ional po en ial deepening and c owding o pa icles
4. Highe densi y →Collision p obabili y inc eases independen ly o po en ial
5. Mo e collisions →Enhanced ene gy edis ibu ion →In e nal ene gy eco e y
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6. In e nal ene gy eco e y →Tempe a u e ise despi e o al ene gy loss ⇒C<0
This sequen ial amewo k cla i ies he physical causali y behind he empe a u e ise obse ed in
sel -g a i a ing ensembles. I highligh s ha bo h po en ial deepening and collisional
ampli ica ion ac oge he o p oduce he coun e in ui i e he mal beha io , p o iding a conc e e
mic oscopic basis o he eme gence o nega i e hea capaci y.
Implica ions
This coun e in ui i e beha io unde lies he he modynamic ins abili y o sel -g a i a ing
sys ems. I explains why g a i a ionally bound sys ems end o unde go co e collapse and halo
expansion, a p ocess ha e en ually p e en s hem om eaching ue he mal equilib ium.
In summa y, nega i e hea capaci y a ises because g a i a ional po en ial ene gy
becomes inc easingly nega i e du ing con ac ion, con e ing pa o his po en ial
ene gy in o kine ic ene gy, which aises he sys em’s empe a u e e en as o al ene gy
dec eases.
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Nega i e Hea Capaci y in Sel -G a i a ing Sys ems
In oduc o y ex goes he e. A wild example pa en he ical e e ence appea s (Con ibu o ,
2023), ollowed by an in- ex sample ci a ion by Book Au ho (2021).
No e ha pa ag aphs a e sepa a ed by a blank line in he edi o . I you do no do his, i
will con inue as a single pa ag aph. This line is echnically on a new line in he edi o , bu will
p in in he same pa ag aph.
Me hod
Pa icipan s
Pa icipan in o ma ion goes he e.
Ma e ials
Wo ds, along wi h a sample able (Table 1).
Table 1
Sample wo ds om his hypo he ical expe imen .
Fi s wo d Second wo d
Yee Yoink
Ho Li
Measu es
Some wo ds abou he measu es used.
Design
Some mo e wo ds
P ocedu e
Desc ip ion o he p ocedu e.
Resul s
Desc ip i e S a is ics
S a is ical wo ds. A demons a i e Figu e 1.
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Figu e 1
The mean ibes o each wo d ype and coun e balanced condi ion o de . E o ba s ep esen
one s anda d e o o he mean.
In e en ial S a is ics
Analy ical wo ds.
Discussion
Discussion wo ds.
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Re e ences
Book Au ho , F. P. (2021). Fancy Pan s Whole Book. So & Fancy Publishing.
Con ibu o , C. (2023). The Ti le o he Chap e . In F. Edi o & S. Edi o (Eds.), The Book Ti le
(pp. 42–69). O he Publishing Place.
