Thermodynamic Computing 1 14 Forward Through Backwards Time by - - PowerPoint PPT Presentation

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Thermodynamic Computing 1 14 Forward Through Backwards Time by - - PowerPoint PPT Presentation

Aug 14, 2022 160 likes •328 views

Thermodynamic Computing 1 14 Forward Through Backwards Time by RocketBoom The 2nd Law of Thermodynamics Total Entropy Clausius inequality S total 0 increases (1865) as time progresses R.Penrose (2010) Cycles of time Once or

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14 1 Forward Through Backwards Time by RocketBoom

Thermodynamic Computing

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Gavin E. Crooks Cycles of time R.Penrose (2010)

The 2nd Law of Thermodynamics

Clausius inequality (1865)

Total Entropy increases as time progresses

∆Stotal ≥ 0

Once or twice I have been provoked and asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold. It was also negative. Yet I was asking something which is about the scientific equivalent of “Have you read a work of Shakespeare's?”

  • - C. P. Snow
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Gavin E. Crooks

Thermodynamic Equilibrium: Future, past and present are indistinguishable

No change in entropy

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Gavin E. Crooks

1 kT = 25 meV = 2.5 kJ/mol 1 natural unit of entropy equivalent to 1 kT of thermal energy T : Temperature (ambient 300 Kelvin) k : Boltzmann’s constant

What is Entropy?

average kinetic energy = 1.5 kT

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Gavin E. Crooks

Trap Bead Actuator Bead Pizeoelectic Actuator Laser Trap Trap Bead Actuator Bead RNA Hairpin

probability

∆Stotal = 1 T

  • W − ∆F
  • temperature

work total entropy change free energy change force length u n f

  • l

d i n g f

  • l

d i n g unfolding Entropy sometimes goes down!

Unfolding of RNA hairpins. (circa 2000)

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Gavin E. Crooks

The (improved) 2nd Law of Thermodynamics

Clausius inequality (1865)

he−∆Stotali = 1

Jarzynski identity (1997)

h∆Stotali 0

∆Stotal = 1 T

  • W − ∆F
  • equality only for

reversible process equality far-from-equilibrium

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Gavin E. Crooks

Free Energy Change Work Inverse Temperature Forward Trajectory Reverse Trajectory Time Phase Space

Fluctuation Theorems: Dissipation breaks time-reversal symmetry

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Gavin E. Crooks

What have we learned?

  • There are exact, general relations valid far-from-equilibrium
  • Trajectories are the primary objects (rather than states)
  • The fluctuations matter
  • Entropy change breaks time quantitatively reversal symmetry
  • Directly relevant at small dissipation
  • Information and entropy are related:

Information flow is as important as work and heat flow.

he−∆Stotali = 1

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Gavin E. Crooks

Position (μm) 10

a b e f c d

5 10 5 10 5 10 5 0.5 −0.5 0.5 −0.5 0.5 −0.5 0.5 −0.5 0.5 −0.5 0.5 −0.5 10 5 10 5 Potential (kT) Position (μm)

Bits are physical

Experimental verification of Landauer’s principle linking information and thermodynamics

Antoine Be ´rut1, Artak Arakelyan1, Artyom Petrosyan1, Sergio Ciliberto1, Raoul Dillenschneider2 & Eric Lutz3{

Erasing 1 bit of information requires at least ln 2 kT energy Thermodynamic entropy and Shannon information are related

Non-equilibrium Theory of erasure see: Esposito (2011)

(2012)

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Gavin E. Crooks

Experimental verification of Landauer’s principle linking information and thermodynamics

Antoine Be ´rut1, Artak Arakelyan1, Artyom Petrosyan1, Sergio Ciliberto1, Raoul Dillenschneider2 & Eric Lutz3{

Erasure time Average heat

4 3 2 1 10 20 30 40 〈Q〉 (kT)

c

τ (s)

But: Thermodynamically reversible computation requires Carnot limit, i.e. infinity long time

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Gavin E. Crooks

Experimental verification of Landauer’s principle linking information and thermodynamics

Antoine Be ´rut1, Artak Arakelyan1, Artyom Petrosyan1, Sergio Ciliberto1, Raoul Dillenschneider2 & Eric Lutz3{

Heat P(Heat) Fluctuations matter! Tradeoff between error, time, and energy

0.15 0.10 0.05 P(Q) Fmax (10−14 N) −2 2 4 Q (kT)

b

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Gavin E. Crooks

Feedback Fluctuation Theorems (c2010)

D e− 1

T (W −∆F )−IE

= 1

Demon-system information

Sagawa & Ueda (2008) Horowitz & Vaikuntanathan (2010)

Research Highlights

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Gavin E. Crooks

Research Highlights Thermodynamics of Prediction Still, Sivak, Bell, Crooks (2012)

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Gavin E. Crooks / 22 14

Research Highlights 1/2

Optimal thermodynamic control Coupled Systems Experiments

Feynman's ratchet

Bang et al (2018)

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Gavin E. Crooks Lahiri, Sohl-Dickstein, Ganguli (2016)

time-dissipation-error tradeoff Thermodynamics uncertainty realtions Self-organization and the generation of complexity

Research Highlights 2/2

  • T. R. Gingrich, J. M. Horowitz, N. Perunov

and J. L. England (2015)

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Gavin E. Crooks / 22 16