geodesic op*mizaon in thermodynamic control...geodesic op*mizaon in thermodynamic control manoa...
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Geodesicop*miza*oninthermodynamiccontrol
ManoaMini-SymposiumonPhysicsofAdap*veComputa*onJanuary7,2019
MikeDeWeesewith:PatrickZulkowski,DibyenduMandal,Ka8eKlymko,NehaWadia,RyanZarcone,DavidSivak,&GavinCrooks
UCBerkeley
0010010110… 1000110101… 1000110101… 1110110101…
Somelong-termgoals:
• Newthermodynamicrela*ons• Predictsignaturesofefficientbiomolecules
• Designop*malcomputa*onaldevices
• Geometricframework
• Op*malbiterasure
• Newgeneraliza*onofgeometricframeworkfromSlowPerturba*onTheory
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TalkOutline
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Geometryinthermodynamics• Longhistory,e.g.:
• “Thermodynamiclength”• Assumedendoreversibility(systeminequilibrium,ifnotsameasenvironment)
• Macroscopicdescrip*on
Weinhold, J Chem Phys 63, 2479 (1975) Ruppeiner, PRA 20, 1608 (1979) Schlögl, Z Phys B 59, 449 (1985) Salamon, Nulton, & Ihrig, J Chem Phys 80, 436 (1984) Salamon & Berry, PRL 51, 1127 (1983) Brody & Rivier, PRE 51, 1006 (1995) …
Geometryinthermodynamics• Microscopicratherthanmacroscopic:
• Extendtononequilibriumsystems(beyondendoreversibility):
• Derivedinthelinearresponseregime• Sinceextended(Mandal&Jarzynski,others)
Crooks, PRL 99, 100602 (2007) Burbea & Rao, J. Multivariate Anal. 12, 575 (1982) Feng & Crooks, PRE 79, 012104 (2009)
Sivak & Crooks, PRL 108, 190602 (2012)
Sivak & Crooks, PRL (2012)
⇒
Linearresp. op*malprotocols=geodesics
Externalcontrol
parameters
Conjugateforces
RiemannianMetric
⇒
Someproper*esofop*malprotocols(inlinearresp.regime):
Sivak & Crooks, PRL (2012)
• Followgeodesics• Requireconstantexcesspower• Independentoftotaldura*onexceptforglobalrescaling
• Canbecalculatedbasedonequilibriumaspectsofsystem
Op*malprotocolsaregeodesics
(Evensimplegeometriescanyieldcomplexop*malprotocolsintermsofthecontrol
parameters)
Onceyouknowthemetric,howdoyoufindgeodesics?
Nosystema*cwaythat’sguaranteedtowork,buttherearetools:• Christoffelsymbols• Geodesicequa*on• Scalercurvature(Ricciscaler;usefulin2-D)• Killingvectorfields(isometries/symmetries)• Tryvariouscoordinatetransforma*onsto
simplifyeqs.,andrecognizefamiliarspaces
1stmodel:Par*cleinop*caltweezers(ordriventorsionpendulum,ornanomechanicaloscil.)
Zulkowski, Sivak, Crooks & DeWeese PRE (2012)
Smallk Lowβ
Largeyo
Time
Time
Largek
Iner*alLangevindynamics,3controlparams:
Highβ
Smallyo
Zulkowski, Sivak, Crooks & DeWeese PRE (2012)
Iner*alLangevindynamics:
withGaussianwhitenoise:
1stmodel:Par*cleinop*caltweezers
1stmodel:Par*cleinop*caltweezers
Ø Decouplingofy0from(β,k)Ø :constantnega*vecurvatureØ hyperbolicgeometryfor(β,k)submanifold
y0y0
β
β k
k
Zulkowski, Sivak, Crooks & DeWeese PRE (2012)
Metrictensor:
Zulkowski, Sivak, Crooks & DeWeese PRE (2012)
Changeofvariables:hyperbolicgeometry
1stmodel:Par*cleinop*caltweezers
1/
1stmodel:Par*cleinop*caltweezers
Zulkowski, Sivak, Crooks & DeWeese PRE (2012)
1/
Op'malpathsarecomplex!
Op*malprotocolcanbemuchmoreefficientthannearbypaths
1/
Notesandopenques*ons:• Canop*mize3paramsatonce(k,y0:Aurell2012;Seifert2007,2008)• Trea*ngβasacontrolparameter;measuring
dissipa*oninunitsofentropy• Whatdothe2conservedquan**esmean?• Aretheremore?(canbeupto6Killingfields)• Whatisfullrangeofapplicabilityforthis
approach?(>lin.resp.&deriv.trunca*on?)• Whatdoesscalarcurvature(R )represent?
(seemsdifferentthanRofGeorgeRuppeiner,butP.S.Krishnaprasadcalc.suggestsdeepconnec*on…)
Op*malbiterasure:asimple,butexactlysolvable,model
asimple,butexactlysolvable,model
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Overdamped,Brownianpar*cleindoublesquarewell;Fokker-Planckforgeometricapproach
2controlparams:
Op*malbiterasure10
Zulkowski & DeWeese PRE (2014)
Flatmanifold!vanisheseverywhereforthis2-Dmodel:
R = 0
Flatmanifold!
Op*malbiterasure10
Zulkowski & DeWeese PRE (2014)
Op*malbiterasure10
Exact: LinearResponse:
Zulkowski & DeWeese PRE (2014)
Op*malbiterasure10
Aurell et al., J Stat Phys (2012) Esposito et al., Europhys Let (2010) Diana, Bagci & Esposito, PRE (2013)
(KistwicethesquareoftheHellingerDistance)
Zulkowski & DeWeese PRE (2014)
Landauer Finitetcost
Beyonderasure10
PL(tf)
PL(0)
−∆𝑆/𝑘𝐵 K
Erasure Zulkowski & DeWeese PRE (2014)
Newgeneraliza*onfromSlowPerturba*onTheory
Wadia, Zarcone, DeWeese, Mandal, in prep.
TimeDependentFokker-PlanckEqua*on
Foker-Planckoperator1stcorrec*ontoequil.dist.
MetricTensorExplicittermstoallorders
Thanks! David David , Gavin Crooks, Sivak
Postdocs: , Gavin Crooks, Vivienne Ming, Paul King Postdocs: Alfonso Dibyendu Mandal, Alfonso Apicella, Mohammad Dastjerdi, Louis Kang Grad Students: Patrick Zulkowski, Neha Wadia, Ryan Zarcone, Katie
Chris Rodgers, Joel Zylberberg , Nicole Carlson, Jesse , Eric , Nicole Carlson, Jesse BattaglinoLivezey, Peter Jascha Battaglino, SohlJascha
, Sarah Thanapirom, Vanessa , Joseph ThurakalCarels
, Sarah MarzenPooneh, Joseph
Thurakal, Charles Frye, Mayur Mudigonda Arnemann , PoonehUndergrads & PostbacksMohammadiara, Pratik Sachdeva, Michael Fang, James Arnemann Undergrads & ,
Postbacks Yerxa, David Pfau, Marvin , Thielk, Vu, Sarah Trevor Dolinajec, Ambika Rustagi, Vu, Sarah
Kochik, Lily Lin, Yassi Sabahi,
Christian Fernandez, Pooja Upadhyaya, Camille Malatt, Yuliy , Daniel Resnick, Jacob Simon, Daniel Cho, Tanling Nancy Hsu, Ramon Martinez, Winward Choy, Carol Pham, Vivek Ayer, , Steven Munn, Jason Zhang, Josh Chong, Amish Shah, Rachel Lim, Charles Choi, Tommy Li, Danielle Jobe, Yuliy , S. Zayd Enam, Steven Munn, Shayaan Abdullah, Doron Reuven, Ali Al Setr, Ahyeon
Hwang, Tepp Ahn, Christopher Bryant, Julian Bacon, Emil , Anna Yap, Julia Wong, Pauldeep Singh, Angie Kim, Celeste Zamora, Marvin Alcantara, Jenna
Pinkham, Nathan Olsy, Bastian Pavlacka Pardede, Ned Udomkesmalee, Peter Dotti, Salman Kahn, Ziyan Feng, Bryon
Pavlacka, Steven Munn, Sharon Lin, Ngoc Huyen Tran Nguyen, Adam Bruce, Trevor Grandpre, Kevin Gutowski, Nikhil Sthalekar, Jason Belling, Kyle Chism, Alison Kim, Bernal Jimenez, Christian Merino, Greg Martin,
Gurubala Kotta, Andrew Berger, Brandon Lazar, Qianjin
Wu, Josh Goldman This material is based upon work supported in part by the US Army Research
Laboratory and the US Army Research Office Under Contract No.W911NF-13-1-0390.
