# Thermodynamic of computing. Fisica dell Energia - a.a. 2017/2018

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1 Thermodynamic of computing Fisica dell Energia - a.a. 2017/2018

2 Landauer principle Minimum amount of energy required greater than zero Let assume the operation of bit reset # of initial states: 2 # of final states: 1

3 Landauer principle S = k B log W Q T S Initial condition: two possible states Final condition: one possible state Heat produced S i = k B log 2 S f = k B log 1 S = S f S i = k B log 2 Q T S = k B T log 2

4 Landauer principle experimental verification The physics of information: from Maxwell s demon to Landauer - Eric Lutz - University of Erlangen-Nürnberg

5 Landauer principle experimental verification Even if you're not burning books, destroying information generates heat. - Sergio Ciliberto

6 Landauer principle experimental verification The physics of information: from Maxwell s demon to Landauer - Eric Lutz - University of Erlangen-Nürnberg

7 Landauer principle experimental verification The physics of information: from Maxwell s demon to Landauer - Eric Lutz - University of Erlangen-Nürnberg

8 Landauer principle experimental verification The physics of information: from Maxwell s demon to Landauer - Eric Lutz - University of Erlangen-Nürnberg

9 Landauer principle experimental verification Jun, Y., Gavrilov, M., & Bechhoefer, J. (2014). High-Precision Test of Landauer s Principle in a Feedback Trap. Physical Review Letters, 113(19),

10 Landauer principle experimental verification Feedback Trap Jun, Y., Gavrilov, M., & Bechhoefer, J. (2014). High-Precision Test of Landauer s Principle in a Feedback Trap. Physical Review Letters, 113(19),

11 Landauer principle experimental verification Erasure protocol Jun, Y., Gavrilov, M., & Bechhoefer, J. (2014). High-Precision Test of Landauer s Principle in a Feedback Trap. Physical Review Letters, 113(19),

12 Landauer principle experimental verification Work series for individual cycles Jun, Y., Gavrilov, M., & Bechhoefer, J. (2014). High-Precision Test of Landauer s Principle in a Feedback Trap. Physical Review Letters, 113(19),

13 Time-dependent study of bit reset

14 Reset on colloidal particles Chiuchiú, D. "Time-dependent study of bit reset." EPL (Europhysics Letters) (2015):

15 Time-dependent study For a fixed τpr with Q(τpr) T S(τpr), study T S(t), Q(t), W (t), E(t). Chiuchiú, D. "Time-dependent study of bit reset." EPL (Europhysics Letters) (2015):

16 MEMS/NEMS Memory Device

17 NEMS Memory Devices Ionescu, Adrian M. "Nano Electro Mechanical (NEM) Memory Devices." Emerging Nanoelectronic Devices (2014):

18 NEMS Memory Devices Ionescu, Adrian M. "Nano Electro Mechanical (NEM) Memory Devices." Emerging Nanoelectronic Devices (2014):

19 NEMS Memory Devices Ionescu, Adrian M. "Nano Electro Mechanical (NEM) Memory Devices." Emerging Nanoelectronic Devices (2014):

20 NEMS Memory Devices

21 NEMS system

22 NEMS system armchair direction 6x1 nm atoms a = 2.42 Å Y = 0.85 TPa T = 10 K Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

23 2-DOF potential landscape Energy (J) A2 A A1 (Å) A2 (Å) 5 Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

24 Reset protocol Objective: move the system from an unknown state to known state ΔS = kb log(2) Qmin = kb T log(2) A1 A1 A2 Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015): A2

25 Reset protocol Quick and dirty: apply a positive force along Z on all atoms WRONG: it is not possible to control the velocity!

26 Reset protocol Quick and dirty: apply a positive force along Z on all atoms

27 Reset protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration f MaxUp f 0Up f MaxDw f 0Dw t 0 t 1 t 2 t 3 t 4 Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

28 t 0 t 1 t 2 t 3 t 4 Reset protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration f MaxUp f 0Up f MaxDw f 0Dw

29 Reset protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

30 Reset protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration 0.4 τ p =110 ns counts 0.2 Q/kBT Q/kBT QL=kBTln2 τp (ns) Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

31 Switch protocol Objective: move the system from a known state to another known state ΔS = 0 Qmin = 0 A1 A1 A2 Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015): A2

32 Switch protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration f MaxUp f 0Up f MaxDw f 0Dw t 0 t 1 t 2 t 3 t 4 t 5 t 6 Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

33 t t t t t t t Switch protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration f MaxUp f 0Up f MaxDw f 0Dw

34 Switch protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

35 Switch protocol Controlled way: apply a set of forces in to gently put the system in the desired configuration 0.4 τ p =210 ns counts 0.2 Q/kBT Q/kBT τp (ns) Neri, I., et al. "Reset and switch protocols at Landauer limit in a graphene buckled ribbon." EPL (Europhysics Letters) (2015):

36 t t t t t t t Switch protocol Wrong way: apply the switch protocol from the wrong initial state f MaxUp f 0Up f MaxDw f 0Dw

37 Switch protocol Wrong way: apply the switch protocol from the wrong initial state Qmin > 2QL

38 Micro-electromechanical memory bit based on magnetic repulsion

39 Micro-electromechanical memory bit based on magnetic repulsion Micro-electromechanical memory bit based on magnetic repulsion, López-Suárez, Miquel and Neri, Igor, Applied Physics Letters, 109, (2016)

40 Micro-electromechanical memory bit based on magnetic repulsion Micro-electromechanical memory bit based on magnetic repulsion, López-Suárez, Miquel and Neri, Igor, Applied Physics Letters, 109, (2016)

41 Micro-electromechanical memory bit based on magnetic repulsion Micro-electromechanical memory bit based on magnetic repulsion, López-Suárez, Miquel and Neri, Igor, Applied Physics Letters, 109, (2016)

42 Micro-electromechanical memory bit based on magnetic repulsion Orders of magnitude above Landauer limit! Micro-electromechanical memory bit based on magnetic repulsion, López-Suárez, Miquel and Neri, Igor, Applied Physics Letters, 109, (2016)

43 Solution: increase the temperature

44 Solution: increase the temperature Neri, Igor, and Miquel López-Suárez. "Heat production and error probability relation in Landauer reset at effective temperature." Scientific Reports 6 (2016).

45 Reset protocol Q=W-ΔU Neri, Igor, and Miquel López-Suárez. "Heat production and error probability relation in Landauer reset at effective temperature." Scientific Reports 6 (2016).

46 Landauer reset with error Neri, Igor, and Miquel López-Suárez. "Heat production and error probability relation in Landauer reset at effective temperature." Scientific Reports 6 (2016).

47 Unconventional computing

48 Robust Soldier Crab Ball Gate Yukio-Pegio Gunji, Yuta Nishiyama, Andrew Adamatzky

49 Robust Soldier Crab Ball Gate OR gate Robust Soldier Crab Ball Gate - Yukio-Pegio Gunji, Yuta Nishiyama, Andrew Adamatzky

50 Robust Soldier Crab Ball Gate AND gate Robust Soldier Crab Ball Gate - Yukio-Pegio Gunji, Yuta Nishiyama, Andrew Adamatzky

51 Robust Soldier Crab Ball Gate Robust Soldier Crab Ball Gate - Yukio-Pegio Gunji, Yuta Nishiyama, Andrew Adamatzky

52 Robust Soldier Crab Ball Gate How much energy? Crabs usually eat algae. Crabs are omnivorous, meaning that they will eat both plants and other animals for sustenance. Energy Content of Algae: 5kcal for 3g Average weight of the crabs was 42g Suppose daily need is 50% of its weight: 21g of algae and thus 35kcal J of energy for daily operating a crab logic gate or 1.7W of power

53 Mechanical logic gate

54 Mechanical logic gate AND gate

55 Mechanical logic gate López-Suárez, M. et al. Sub-kBT micro-electromechanical irreversible logic gate. Nat. Commun. 7:12068 (2016)

56 Mechanical logic gate Ω0 Ω1 López-Suárez, M. et al. Sub-kBT micro-electromechanical irreversible logic gate. Nat. Commun. 7:12068 (2016)

57 Mechanical logic gate López-Suárez, M. et al. Sub-kBT micro-electromechanical irreversible logic gate. Nat. Commun. 7:12068 (2016)

58 Mechanical logic gate ΔU = W Q = 0 López-Suárez, M. et al. Sub-kBT micro-electromechanical irreversible logic gate. Nat. Commun. 7:12068 (2016)

59 Mechanical logic gate López-Suárez, M. et al. Sub-kBT micro-electromechanical irreversible logic gate. Nat. Commun. 7:12068 (2016)

60 Full adder López-Suárez, M. et al. Sub-kBT micro-electromechanical irreversible logic gate. Nat. Commun. 7:12068 (2016)

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