geodesic op*mizaon in thermodynamic control...geodesic op*mizaon in thermodynamic control manoa...

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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W

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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.