Minimization of entropy production in separate and connected process units

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BDCEGFIHJCLKMFNEGFICOPFIQRKMKTSUFJVQWEXHJHNKMY@HNZ

[\KT]O_^JHJWKTS`HZ_acbdCLKTWEGFJHJ^Je

f\ZP^JgdKThEiO_SjSEXklKT^NFJEXHme<Z_acnAoTEGKTSLoMK*O_SLYpBqKMoNCSLZPrGZPhe

EXSp]O_^JHJEiO_rsatVrvuLrXrXWKTSwH\Z_axHJCLKy^NKMz`VEX^NKTWKTSwHNF{a|ZP^

HJCLK8fZP^Jg}KThEiO_S~OPoOPYKTWEGo YKTh^NKMK

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f{’„•–Žw—™˜8Bš^NZPSLY™CLKTEXW

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BDCEGFdHJCLKMFJEGFdgdZPVrGY5SLZPHdCOklKK ™EGFJHNKMY>gdKT^NKEXHdSLZPHcatZP^}HJCLKIuLSO_SLoTEiO_rsFJV]]RZP^JHDZRKT^NKMY

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HJCLK]^NZPh^œO_W0a|ZP^ˆatVSLYLO_WKTSwHœO_rR^NKMFNKO_^NoœC@FJ]”ZPSLFœZP^NKMYQweHJCLK\f\ZP^JgdKThEiO_S

‹ oOPYKTW eUZ_a}nAoTEGKTSLoMK+O_SLYšKTHJHNKT^NFyO_SLY~n`HœO_HNZPEXrƒdHJCO_S~O_rXrqZ_a HJCLZFNK EXSwklZPrXklKMYUatZP^

]^NZ‘k`EGY™EXShWK8HJCLK8ZP]]”ZP^JHJVSEXHme<HNZgdZP^J@ZPS@HJCEGFHJCLKMFNEGF

LZP^@QRKTEXSh$W e"FJV]RKT^JkAEGFNZP^pY™V^JEXSh$HJCLK'a|ZPV^UO_SLY O:CO_rvaelKO_^pEXH@HNZ`ZP"HNZ:uLSEGFJC

HJCEGF}]^NZ_JKMoTH ƒˆFJEXSLoMKT^NKTrXeHJCO_S ^NZ_acn`EXhSLKy}JKTrGFJHJ^JV]cn`CLK\HœO_VhCwHIWK\HJCLKyO_^JHIZ_a

FNoTEGKTS`HJEvuoc^NKMFœKO_^NoNCEXS*hlKTSLKT^œO_rLO_SLY HJCLK uKTrGY+Z_aLSLZPSLKMzwVEXrXEXQ^JEXVWHJCLKT^JWZAY™e`SO_WEGoMFxEXS

]O_^JHJEGoTVriO_^\KT^ SLKTklKT^Š’ KTSLY™EXSh8K sZP^JHqHNZVSLYKT^NFJHœO_SLY HJCLKˆatVSLYLO_WKTSwHœO_rWKMoœCO_SEGFJWF

Z_a{f‡O_HJV^NK5EGFOFNZPV^NoMK5Z_a{h^NKO_HEXSLFJ]EX^œO_HJEGZPS=ƒ‡CLZP]RK g}K>W OeoMZPS`HJEXSwVLK<gdZP^JAEXSh

HNZPhlKTHJCLKT^EXSUHJCLK‡elKO_^NFHNZoMZPWK

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O_SLY6a|ZP^<FNCO_^JEXSh CO_]]EXrXe"Z_a+CEGF@FNKMKTWEXShrXe6EXS™uLSEXHNK'ASLZgIrGKMY™hlK Z_a ]Cwe™FJEGoMFpO_SLY

W O_HJCLKTW O_HJEGoMF LV^JHJCLKT^JWZP^NK ƒxO_W;h^œO_HNK¡aVratZP^ˆHJCLK\OPFNFJEGFJHœO_SLoMK{ƒqCOklKhlZPHJHNKTS a^NZPW

^NZ_a žqŠ›P^JS\O–a|FJ–ŠZPrGY<ZPSpoTriOPFNFJEGoO_r HJCLKT^JWZ`Y™eASO_WEGoMF{EXS@HJEXWKMFZ_a oMZPS™atVLFJEGZPS

LZP^hEXkAEXSh'HJCLK>]^NZ_JKMoTHO_S EXSLY™VLFJHJ^JEiO_rIEXS]VH

ƒyHJCO_S:‚{ZPhlKT^\O_SLFœKTS O_H n`HœO_HNZPEXr

‚KMFNKO_^NoNC6b}KTS`HNKT^ O_H‚{ZPHJklZPrXr B ^NZPSLY™CLKTEXW!"K<FJV]]rXEGKMY$SLKMoMKMFNFœO_^Je EXS™a|ZP^JW O_HJEGZPS

O_QRZPVH HJCLKD]^NZP]O_SLKYKTCwe™Y™^NZPhlKTSO_HJEGZPS5]^NZ`oMKMFNFˆO_SLYCLKTrX]RKMYlKMKT]EXSh8HJCLKD^JEXhC`H a|Z`oTVLF

ZPS@HJCLKy]^NZAoMKMFNFZP]HJEXWE$#‘O_HJEGZPS]O_^JH

‹ rXr HJCLK^NKMFJVrXHNFyHJCO_H O_^NK]^NKMFœKTSwHNKMY EXS=HJCEGF8HJCLKMFJEGFygdKT^NK ZPQHœO_EXSLKMY=Qwe']RKT^ŠatZP^JWEXSh

S`VWKT^JEGoO_r\oO_rGoTVriO_HJEGZPSLF O_SLY6O=FJHœO_QrGKO_SLY$gdKTrXrv’KMz`VEX]]”KMY"oMZPW]VHNKT^a“OPoTEXrXEXH e-O_H

[‡KT]O_^JHJWKTSwHDZ_a bdCLKTWEGFJHJ^JeW OPYKIHJCLK{oO_rGoTVriO_HJEGZPSLFd]RZFNFJEXQrGK ƒxO_W;YKMKT]rXeh^œO_HNK¡aVr

HNZ>B KT^tJK ž}^JVklZPrXrqatZP^‡O_]]^NKMoTEiO_HJEXSh5HJCLK*kPO_rXVLK Z_acoMZPW]VHNKT^NF\EXS~FNoTEGKTS`HJEvuo*g}ZP^J OPF

g}KTrXr}OPFya|ZP^8oT^NKO_HJEXSh=O5a^JEGKTSLY™rXe O_HJWZFJ]CLKT^NK<O_WZPShUHJCLK FJHœO%-O_H*[‡KT]O_^JHJWKTSwHZ_a

bdCLKTWEGFJHJ^Je&

‹ WZPShW*e@oMZPrXrGKO_hVLKMF ƒcgIEGFJCpHNZHJCO_S<† EXkAEXSLY!'lZPCO_SSLKMFNFNKTSEXS@]O_^JHJEGoTVriO_^}€V^

oMZPVS`HJrGKMFNF FNoTEGKTSwHJEvuoDY™EGFNoTVLFNFNEGZPSLF ^NKO_rXrXe*oMZPS`HJ^JEXQVHNKMYHNZFNCO_]”KcW*e8HJCLZPVhC`HNF ZPS W O_HŠ’

HNKT^NF{^NKTriO_HNKMYpHNZ KTS`HJ^NZP]we@]^NZAY™VLoTHJEGZPSWEXSEXWE$#‘O_HJEGZPSLF({…‡KTrGKTEXSYK8Z`KTEJKT^\O_SLY O_^NF

fVWWKMYLO_r

gICLZ<QRZPHJC=gdZP^JlKMY ZPS FJVQ™JKMoTHNF‡^NKTriO_HNKMY=HNZ<W eHJCLKMFJEGF

riOMe~HJCLK+atZPVS™’

YLO_HJEGZPS5a|ZP^dHJCLK\]^NKMFNKTS`H}g}ZP^J) ƒˆHJCO_S HJCLKTW9Q”ZPHJC>a|ZP^dHJCLKTEX^IK sZP^JH ƒ H}^NKO_rXrXe W OPYK

OY™E*sKT^NKTSLoMK

BDCO_S™F HNZyO_rXrLZ_a W*e a|ZP^JWKT^ O_SLY]^NKMFœKTSwHˆoMZPrXrGKO_hVLKMFdO_H HJCLKI[‡KT]O_^JHJWKTSwHdZ_asbdCLKTW’

EGFJHJ^Je+a|ZP^ˆHJCLKTEX^dK sZP^JHˆEXS>W O_`EXSh HJCLK{YLO_EXrXerXEvatK\O_HˆHJCLK{YKT]O_^JHJWKTS`HDWZP^NK{KTSPJZewO_QrGK

O_^NF*† ^JEX”yƒ{WEGFNFyHJCLZFNKYLO_EXrXe'oNCLKMFœF*O_SLY oO_lKFNKMFNFNEGZPSLF‡gdKVLFNKMY'HNZ<COklKQRK¡atZP^NK

rXEva|K\hlZPHIHNZ`ZFNKT^JEGZPVLF ƒ}O_rGFNZ+gIEGFJC<HNZHJCO_S W e>]O_^NKTS`HNFDatZP^DHNKOPoœCEXShWK‡HJCLK‡kPO_rXVLK

Z_a{KMY™VLoO_HJEGZPS6EXHJCLZPVH+EXH

ƒ\gdZPVrGY:SLZPH+COMklK>hlZPSLK HNZ'O@VSEXklKT^NFJEXHme EXS:HJCLKuL^NFJH

]riOPoMK

xEXSO_rXrXe ƒDCOPYpHJCLK8h^NKO_Ha|ZP^JHJVSLK8HNZg}ZP^JOPFOhVLKMFJH{^NKMFœKO_^NoNCLKT^8O_H{HJCLK f\O_HJEGZPSO_r

ƒmSLFJHJEXHJVHNKZ_a ‹ Y™kPO_SLoMKMY ƒmSLY™VLFJHJ^JEiO_rdnAoTEGKTSLoMK O_SLY=BqKMoNCSLZPrGZPhe EXS BqFJVAVQO 'wO_]O_S

ƒmSHJCLK† SLKT^Jhe`’ K oTEGKTSwHbdCLKTWEGoO_ršn`eAFJHNKTWF}…\^NZPV]

rGKOPY Qwe[\^xf‡O_O_EXg}O

ƒxFJ]RKTSwH

uLklK~gdZPSLYKT^ŠatVr‡WZPSwHJCLFBDCLK~CLZFJ]EXHœO_rXEXHme"O_SLY"hlKTSLKT^NZFJEXHme6ƒ^NKMoMKTEXklKMY6at^NZPW&W e

oMZPrXrGKO_hVLKMF\O_SLY<a^JEGKTSLYF{HJCLKT^NKyg}OPFHJ^JVrXe5EXSLoT^NKMY™EXQrGKdB ZHJCLKTW ƒdFœOe”

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BDCLK<ZPQ™JKMoTHJEXklK5Z_aHJCEGFHJCLKMFJEGF+g}OPFHNZUaV^JHJCLKT^YKTklKTrGZP]$OWKTHJCLZ`YZPrGZPhe atZP^WEXSEv’

WE$#MEXShHJCLK\KTSwHJ^NZP]we5]^NZAY™VLoTHJEGZPS<Z_axFJEXShrGK\O_SLY<oMZPSSLKMoTHNKMY<oNCLKTWEGoO_rs]^NZAoMKMFNF}VSEXHNF

"CLKTSoœCLKTWEGoO_rq]^NZAoMKMFNF{KMz`VEX]WKTSwH‡EGFYKMFJEXhSLKMYO_SLYZP]”KT^œO_HNKMY'O_H{HJCLK*rGZgdKMFNH\KTS™’

HJ^NZP]`e ]^NZAY™VLoTHJEGZPSp]”ZFœFJEXQrGK HJCLK\KTSLKT^Jhe<K oTEGKTSLoTe<Z_aqHJCLK‡KMzwVEX]WKTS`HEGFIKTSCO_SLoMKMY

K+COMklKatZPVSLYa|ZP^‡FNEXShrGK]^NZ`oMKMFNF‡VSEXHNF‡HJCO_HyHJCLKKTS`HJ^NZP]we']^NZAY™VLoTHJEGZPS oMZPVrGY=Q”K

^NKMY™VLoMKMYUgIEXHJCpV]pHNZ Œ–’“Žw hEXklKTSUHJCLK8YKTh^NKMKMF\Z_aqat^NKMKMYZPW EXSUHJCLK8ZP]HJEXWE$#‘O_HJEGZPS

ƒmS']^NZ`oMKMFNFœKMF ZPV^y^NKMFJVrXHNFyEXSLY™EGoO_HNKMY HJCO_H*KTklKTS=QEXhhlKT^8^NKMY™VLoTHJEGZPSLF*gdKT^NK]RZFNFJEXQrGK

BDCLK5FJHœO_HNKMFZ_a{WEXSEXW*VW KTS`HJ^NZP]we:]^NZ`Y™VLoTHJEGZPS g}KT^NK@FJHJVLY™EGKMY:O_SLY:EXW]RZP^JHœO_SwH]O–’

^œO_WKTHNKT^NF a|ZP^ ZPQHœO_EXSEXSh=FJEXhSEvuoO_SwH^NKMY™VLoTHJEGZPSLF+EXS:HJCLK>KTS`HJ^NZP]we ]^NZAY™VLoTHJEGZPS:gdKT^NK

EGYKTS`HJEvuKMY žDZPHJC=a^NZPW FNVLFJHœO_EXSO_QEXrXEXH e O_SLY=KMoMZPSLZPWEGoO_rckAEGKTgI]RZPEXSwHNF8ASLZgIrGKMY™hlK>Z_a

KTSLKT^Jhe<K oTEGKTSwH\YKMFJEXhSO_SLYpZP]RKT^œO_HJEGZPSO_^NKyEXW]RZP^JHœO_SwH

ƒmSpFNZPWK8Z_a HJCLK8FJe™FJHNKTWFIg}K8FJHJVLY™EGKMY SLZPSLKMz`VEXrXEXQ^JEXVW HJCLKT^JWZAY™eASO_WEGoMF{gDOPFVLFNKMY

HNZ WZ`YKTrHJCLKUKTSwHJ^NZP]`e-]^NZAY™VLoTHJEGZPSƒmS(bdCO_]HNKT^@Œ gdKhwOMklK'O=Q^JEGK¡a8EXSwHJ^NZAY™VLo¡’

HJEGZPS/HNZ Y™E*sKT^NKTSwHpEXSLY™VLFNHJ^JEiO_r O_]]rXEGoO_HJEGZPSLFUZ_a+SLZPSLKMzwVEXrXEXQ^JEXVW HJCLKT^JWZ`Y™eASO_WEGoMF

BDCLK>rXEXS QRKTHgdKMKTS rGZAoO_rDHJ^œO_SLFJ]RZP^JH ]CLKTSLZPWKTSO=O_SLY ZklKT^œO_rXrIFJe™FJHNKTW YKMFNoT^JEX]HJEGZPS

W O_lKMFISLZPSLKMz`VEXrXEXQ^JEXVW HJCLKT^JWZAY™e`SO_WEGoMF\O+VLFNK¡atVr”HNZAZPrRa|ZP^}VSLYKT^NFNHœO_SLY™EXSh>YKMFJEXhS

Z_a oNCLKTWEGoO_rq]^NZ`oMKMFNFVSEXHNF

KyYKTklKTrGZP]RKMYpHJCLKyWKTHJCLZAYZPrGZPhe@Z_axWEXSEXWE$#‘O_HJEGZPS'Z_a KTSwHJ^NZP]we@]^NZAY™VLoTHJEGZPSUEXSFNKTkw’

KT^œO_rxFJHNKT]LF xEX^NFJH g}K+O_SO_rXe #KMY~O_SLYZP]HJEXWE$#KMYUHJCLK KTSwHJ^NZP]`eU]^NZAY™VLoTHJEGZPS~Z_aˆFJEXShrGK

VSEXHNF<B gdZ O_rXHNKT^JSO_HJEXklKoMZPSLoMKT]HNFZ_ayOPY™EiO_QO_HJEGoUY™EGFJHJEXrXriO_HJEGZPSIY™EiO_QO_HJEGoUO_SLY CLKO_HŠ’

EXS`HNKTh^œO_HNKMY6Y™EGFJHJEXrXriO_HJEGZPS

gdKT^NK~O_SO_rXe #KMY(O_SLY-ZP]HJEXWE$#KMY"EXS(bdCO_]HNKT^@£=HNZ:¤/ƒ S

Y™EiO_QO_HJEGo Y™EGFJHJEXrXriO_HJEGZPS CLKO_H{K oNCO_ShlK*EGF{O_rXrGZg}KMY~O_rGZPSh>HJCLK8oMZPrXVWS O_SLYpEXHEGFIHJCEGF

a|KO_HJV^NKDHJCO_H EXSLoT^NKOPFNKMF HJCLKKTSLKT^JheK oTEGKTSLoTeZ_a HJCLKIY™EGFJHJEXrXriO_HJEGZPS>oMZPrXVWS ƒ S bdCO_]™’

HNKT^ £

gdK a|ZPVSLYyCLZ‘gO}hEXklKTS O_^NKOIZ_a™CLKO_HšHJ^œO_SLFŠa|KT^ FJCLZPVrGYyQRK ZP]HJEXW O_rXrXeyY™EGFJHJ^JEXQVHNKMY

O_WZPSh>HJCLK8HJ^œOMe™FEXS~OoMZPrXVWS~FNKT]O_^œO_HJEXSh@OWE*™HJV^NK*Z_aˆ]^NZP]weArGKTSLKO_SLYp]^NZP]O_SLK

BDCLK\^NKMFJVrXHNFIFJCLZ‘gdKMY@HJCO_HICLKO_HK oNCO_ShlK‡gDOPFIWZFJHDEXW]RZP^JHœO_SwH{ZPS<HJCLK‡HJ^œOMe™FIoTrGZFNK

HNZUHJCLK ^NKTQRZPEXrGKT^O_SLY:oMZPSLYKTSLFNKT^~ƒ S bdCO_]HNKT^Ž'O_SLY ¤

gdK5FJHJVLY™EGKMY CLZ‘g9HJCLK>KTS™’

HJ^NZP]`e~]^NZAY™VLoTHJEGZPS Z_a{O5CLKO_HŠ’“EXSwHNKTh^œO_HNKMY Y™EGFJHJEXrXriO_HJEGZPSoMZPrXVWSFNKT]O_^œO_HJEXShQ”KTS #KTSLK

O_SLY6HNZPrXVLKTSLK~g}OPF5EXSLVLKTSLoMKMY(Qwe-oœCO_ShEXSh H g}ZEXW]RZP^JHœO_SwH@FJe™FJHNKTW ]O_^œO_WKTHNKT^NF

BDCLK‡HmgdZ]O_^œO_WKTHNKT^NFgdKT^NK8HJCLKy^œO_HJEGZQRKTH gdKMKTSHJCLKy]^NKMFNFJV^NK8EXS@HJCLKy^NKMoTHJEvaeAEXSh>O_SLY

FJHJ^JEX]]EXShpFœKMoTHJEGZPS O_SLY'HJCLKHNZPHœO_rˆ^œO_HNKZ_adCLKO_HyHJ^œO_SLFŠa|KT^y]RKT^8yKTrXk`EXS ƒS

bdCO_]HNKT^Ž gDOPFKTklKTSrXepY™EGFJHJ^JEXQVHNKMYEXSUHJCLK oMZPrXVWSIBDCLK8^NKMFJVrXHNF\FJCLZ‘gdKMY

HJCO_H8HJCLKT^NKg}OPFO_S V]]”KT^+O_SLY O<rGZg}KT^ QRZPVSLY ZPS HJCLK]^NKMFNFJV^NK^œO_HJEGZ

atZP^*gICEGoNC

HJCLK{CLKO_HŠ’“EXSwHNKTh^œO_HNKMY<oMZPrXVWS>COPY<O‡rGZ‘gdKT^IKTSwHJ^NZP]`e]^NZ`Y™VLoTHJEGZPS5HJCO_S5HJCLKOPY™EiO_QO_HJEGo

oMZPrXVWS ‹ rGZ‘gdKT^\Q”ZPVSLYg}OPF‡O_rGFNZatZPVSLYZPS IƒmS'bdCO_]HNKT^y¤ gdKO_rXrGZg}KMY

HJCLK RHNZ Y™EGFJHJ^JEXQVHNK‡EXHNFœKTrvaqEXS@O_S<ZP]HJEXW O_rsgDOMe&dBDCEGF}KTSO_QrGKMY@KTklKTS<rGZ‘gdKT^{KTS™’

HJ^NZP]`e>]^NZAY™VLoTHJEGZPSLF{O_SLY<gIEGYKTSLKMY<HJCLK‡^œO_ShlKyZ_a HJCLK‡HmgdZ]O_^œO_WKTHNKT^NFIa|ZP^DgICEGoNC@HJCLK

CLKO_HŠ’“EXS`HNKTh^œO_HNKMY@Y™EGFJHJEXrXriO_HJEGZPS>oMZPrXVWS5]”KT^Ša|ZP^JWKMYQRKTHJHNKT^cHJCO_S>HJCLKOPY™EiO_QO_HJEGo

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FˆEXS

bdCO_]HNKT^{£ gdKa|ZPVSLY5HJCO_H}CLKO_HK oNCO_ShlK‡gDOPFDWZFJH}EXW]”ZP^JHœO_S`H{oTrGZFNKHNZ HJCLK‡oMZPS™’

YKTSLFNKT^ˆO_SLY ^NKTQ”ZPEXrGKT^ BDCEGFxW OPYK}VLFx]^NZP]”ZFNKIO{SLKTg YKMFJEXhS*a|ZP^xHJCLKdCLKO_HŠ’“EXS`HNKTh^œO_HNKMY

Y™EGFJHJEXrXriO_HJEGZPS=oMZPrXVWS

gIEXHJC~CLKO_HHJ^œO_SLFJatKT^\Q”KTHmgdKMKTS=HJCLK HNZP]WZFJH8O_SLYUQRZPHJHNZPWWZFJH

HJ^œOeAFZPSrXe&ˆBDCEGFKTSO_QrGKMY<atV^JHJCLKT^^NKMY™VLoTHJEGZPSLFEXS@HJCLK8KTSwHJ^NZP]`e@]^NZ`Y™VLoTHJEGZPS

BDCLK\SLK ™H}FJHNKT]5EXS5HJCLK\YKTklKTrGZP]WKTS`HIg}OPFDHNZ+FJHJVLY™e FNKTklKT^œO_r”VSEXHNF}EXS@oMZPSSLKMoTHJEGZPSˆƒS

bdCO_]HNKT^‡¢

gdK8WEXSEXWE$#KMYUHJCLK8KTSwHJ^NZP]`e@]^NZ`Y™VLoTHJEGZPS~Z_a O+CLKO_HK ™oœCO_ShlKT^

O+]rXVhP’

Z‘g/^NKOPoTHNZP^

O_SLYpO CLKO_HK ™oœCO_ShlKT^EXS@FNKT^JEGKMF BDCEGFDg}OPFO*]^NKT]O_^œO_HNZP^Je@FJHJVLY™e atZP^

HJCLKdriO_^JhlKT^q]^NZAoMKMFNFxZP]HJEXWE$#‘O_HJEGZPSEXSbdCO_]HNKT^c• qž}eyFJCEvatHJEXShCLKO_HxHJ^œO_SLFŠa|KT^šat^NZPW HJCLK

^NKOPoTHNZP^8HNZpHJCLKCLKO_H*K ™oœCO_ShlKT^*V]™’|at^NZPSwH HJCLKKTSwHJ^NZP]`e=]^NZ`Y™VLoTHJEGZPS gDOPFy^NKMY™VLoMKMY

ƒmH{gDOPF‡O_rGFœZa|ZPVSLYUHJCO_H\HJCLKO_W*QEGKTSwHyHNKTW]RKT^œO_HJV^NK+]^NZ_uLrGKO_rGZPSh5HJCLK ^NKOPoTHNZP^\g}OPF

Z_a rGKMFNFIEXW]RZP^JHœO_SwHHNZHJCLK8KTSwHJ^NZP]`e@]^NZ`Y™VLoTHJEGZPS

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