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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
A sel -g a i a ing sys em, such as a s a clus e o molecula cloud, exhibi s an in iguing
he modynamic p ope y known as nega i e hea capaci y. This means ha when he sys em loses
ene gy, i s in e nal empe a u e inc eases, which is con a y o o dina y he modynamic in ui ion.
Physical O igin
Fo a sys em bound by g a i y, he o al ene gy is gi en by
E=K+U,(1)
whe e Kis he kine ic ene gy and Uis he g a i a ional po en ial ene gy, U∝−GM2
R. When he
sys em adia es ene gy (dE <0), he adius Rdec eases due o g a i a ional con ac ion, making
Umo e nega i e. Since K=E−U, he dec ease in Eleads o an inc ease in K, which
co esponds o a highe empe a u e:
dE <0⇒dT >0.(2)
Thus, he hea capaci y Csa is ies
C=dE
dT <0,(3)
indica ing ha he sys em hea s up as i loses ene gy.
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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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.
