GOPAL, Ashwin ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Massimiliano ESPOSITO
ESPOSITO, Massimiliano ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Freitas, Nahuel
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Thermodynamic cost of precise timekeeping in an electronic underdamped clock
D. Brouwer, The accurate measurement of time, Phys. Today 4 (8), 6 (1951) 0031-9228 10.1063/1.3067337.
J. Jespersen and J. Fitz-Randolph, From Sundials to Atomic Clocks: Understanding Time and Frequency (Courier Corporation, North Chelmsford, Massachusetts, 1999).
A. Thomson, Time and Timekeepers (T. & W. Boone, London, UK, 1842).
R. Li, K. Gibble, and K. Szymaniec, Improved accuracy of the NPL-CsF2 primary frequency standard: Evaluation of distributed cavity phase and microwave lensing frequency shifts, Metrologia 48, 283 (2011) 0026-1394 10.1088/0026-1394/48/5/007.
Y. Cao, H. Wang, Q. Ouyang, and Y. Tu, The free-energy cost of accurate biochemical oscillations, Nat. Phys. 11, 772 (2015) 1745-2473 10.1038/nphys3412.
R. Marsland III, W. Cui, and J. M. Horowitz, The thermodynamic uncertainty relation in biochemical oscillations, J. R. Soc., Interface 16, 20190098 (2019) 1742-5689 10.1098/rsif.2019.0098.
A. C. Barato and U. Seifert, Cost and precision of Brownian clocks, Phys. Rev. X 6, 041053 (2016) 2160-3308 10.1103/PhysRevX.6.041053.
P. Erker, M. T. Mitchison, R. Silva, M. P. Woods, N. Brunner, and M. Huber, Autonomous quantum clocks: Does thermodynamics limit our ability to measure time Phys. Rev. X 7, 031022 (2017) 2160-3308 10.1103/PhysRevX.7.031022.
G. Milburn, The thermodynamics of clocks, Contemp. Phys. 61, 69 (2020) 0010-7514 10.1080/00107514.2020.1837471.
A. N. Pearson, Y. Guryanova, P. Erker, E. A. Laird, G. A. D. Briggs, M. Huber, and N. Ares, Measuring the thermodynamic cost of timekeeping, Phys. Rev. X 11, 021029 (2021) 2160-3308 10.1103/PhysRevX.11.021029.
P. Pietzonka, Classical pendulum clocks break the thermodynamic uncertainty relation, Phys. Rev. Lett. 128, 130606 (2022) 0031-9007 10.1103/PhysRevLett.128.130606.
A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015) 0031-9007 10.1103/PhysRevLett.114.158101.
J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2020) 1745-2473 10.1038/s41567-019-0702-6.
G. Falasco, M. Esposito, and J.-C. Delvenne, Unifying thermodynamic uncertainty relations, New J. Phys. 22, 053046 (2020) 1367-2630 10.1088/1367-2630/ab8679.
J. M. Horowitz and T. R. Gingrich, Proof of the finite-time thermodynamic uncertainty relation for steady-state currents, Phys. Rev. E 96, 020103 (R) (2017) 2470-0045 10.1103/PhysRevE.96.020103.
C. Dieball and A. Godec, Direct route to thermodynamic uncertainty relations and their saturation, Phys. Rev. Lett. 130, 087101 (2023) 0031-9007 10.1103/PhysRevLett.130.087101.
P. Helms and D. T. Limmer, Stochastic thermodynamic bounds on logical circuit operation, arXiv:2211.00670.
T. Van Vu and Y. Hasegawa, Uncertainty relations for underdamped Langevin dynamics, Phys. Rev. E 100, 032130 (2019) 2470-0045 10.1103/PhysRevE.100.032130.
J. S. Lee, J.-M. Park, and H. Park, Universal form of thermodynamic uncertainty relation for Langevin dynamics, Phys. Rev. E 104, L052102 (2021) 2470-0045 10.1103/PhysRevE.104.L052102.
L. P. Fischer, H.-M. Chun, and U. Seifert, Free diffusion bounds the precision of currents in underdamped dynamics, Phys. Rev. E 102, 012120 (2020) 2470-0045 10.1103/PhysRevE.102.012120.
A. Wang, B. H. Calhoun, and A. P. Chandrakasan, Sub-Threshold Design for Ultra Low-Power Systems (Springer, 2006), Vol. 95.
J. B. Johnson, Thermal agitation of electricity in conductors, Phys. Rev. 32, 97 (1928) 0031-899X 10.1103/PhysRev.32.97.
H. Nyquist, Thermal agitation of electric charge in conductors, Phys. Rev. 32, 110 (1928) 0031-899X 10.1103/PhysRev.32.110.
N. Freitas, J.-C. Delvenne, and M. Esposito, Stochastic and quantum thermodynamics of driven RLC networks, Phys. Rev. X 10, 031005 (2020) 2160-3308 10.1103/PhysRevX.10.031005.
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, Netherlands, 1992), Vol. 1.
R. Sarpeshkar, T. Delbruck, and C. A. Mead, White noise in MOS transistors and resistors, IEEE Circuits Devices Mag. 9, 23 (1993) 8755-3996 10.1109/101.261888.
R. Landauer, Solid-state shot noise, Phys. Rev. B 47, 16427 (1993) 0163-1829 10.1103/PhysRevB.47.16427.
Y. Cui, G. Niu, A. Rezvani, and S. S. Taylor, Measurement and modeling of drain current thermal noise to shot noise ratio in 90 nm CMOS, in Proceedings of the 2008 IEEE Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems (IEEE, 2008), pp. 118-121.
N. Freitas, J.-C. Delvenne, and M. Esposito, Stochastic thermodynamics of nonlinear electronic circuits: A realistic framework for computing around (Equation presented), Phys. Rev. X 11, 031064 (2021) 2160-3308 10.1103/PhysRevX.11.031064.
C. Y. Gao and D. T. Limmer, Principles of low dissipation computing from a stochastic circuit model, Phys. Rev. Res. 3, 033169 (2021) 2643-1564 10.1103/PhysRevResearch.3.033169.
M. H. Devoret, D. Esteve, H. Grabert, G.-L. Ingold, H. Pothier, and C. Urbina, Effect of the electromagnetic environment on the coulomb blockade in ultrasmall tunnel junctions, Phys. Rev. Lett. 64, 1824 (1990) 0031-9007 10.1103/PhysRevLett.64.1824.
C. Wasshuber, Computational Single-Electronics (Springer Science & Business Media, Berlin, Germany, 2001).
J. Tucker, Complementary digital logic based on the "Coulomb blockade," J. Appl. Phys. 72, 4399 (1992) 0021-8979 10.1063/1.352206.
A. Gopal, M. Esposito, and N. Freitas, Large deviations theory for noisy nonlinear electronics: CMOS inverter as a case study, Phys. Rev. B 106, 155303 (2022) 2469-9950 10.1103/PhysRevB.106.155303.
P. Zheng, Ph.D. thesis, University of California, Berkeley, 2016.
M. Hofheinz, Ph.D. thesis, Université Joseph-Fourier-Grenoble I, 2006.
M. A. Kastner, The single-electron transistor, Rev. Mod. Phys. 64, 849 (1992) 0034-6861 10.1103/RevModPhys.64.849.
P. Fallahi, A. C. Bleszynski, R. M. Westervelt, J. Huang, J. D. Walls, E. J. Heller, M. Hanson, and A. C. Gossard, Imaging a single-electron quantum dot, Nano Lett. 5, 223 (2005) 1530-6984 10.1021/nl048405v.
Consider a sequence of voltages (Equation presented) where (Equation presented) is the voltages before the (Equation presented) tick. In such a situation, the three consecutive increments are given as (Equation presented), (Equation presented), and (Equation presented), where we have used the alternating nature of the coarse-grained states (Equation presented) and set (Equation presented) for simplicity. Since one of the voltage repeats for any two consecutive increments, there will be a non-zero covariance between these terms. These covariances are given as (Equation presented) and (Equation presented), where the sign will depend on the coarse-grained state (Equation presented). Taking the sum of all such covariances, the total variance of the counter given (Equation presented) ticks is given as (Equation presented).
A. Beckers, F. Jazaeri, and C. Enz, Characterization and modeling of 28-nm bulk CMOS technology down to 4.2 K, IEEE J. Electron Devices Soc. 6, 1007 (2018) 2168-6734 10.1109/JEDS.2018.2817458.
A. L. M. Beckers, Cryogenic MOSFET Modeling for Large-Scale Quantum Computing, Tech. Rep. (EPFL, 2021).
E. Irmak, I. Colak, O. Kaplan, and N. Guler, Design and application of a novel zero-crossing detector circuit, in Proceedings of the 2011 International Conference on Power Engineering, Energy and Electrical Drives (IEEE, 2011), pp. 1-4.
L. Y. Gorelik, A. Isacsson, M. V. Voinova, B. Kasemo, R. I. Shekhter, and M. Jonson, Shuttle mechanism for charge transfer in Coulomb blockade nanostructures, Phys. Rev. Lett. 80, 4526 (1998) 0031-9007 10.1103/PhysRevLett.80.4526.
C. W. Wächtler, P. Strasberg, S. H. Klapp, G. Schaller, and C. Jarzynski, Stochastic thermodynamics of self-oscillations: The electron shuttle, New J. Phys. 21, 073009 (2019) 1367-2630 10.1088/1367-2630/ab2727.
U. Seifert, Generalized einstein or Green-Kubo relations for active biomolecular transport, Phys. Rev. Lett. 104, 138101 (2010) 0031-9007 10.1103/PhysRevLett.104.138101.
D. A. Bagrets and Y. V. Nazarov, Full counting statistics of charge transfer in Coulomb blockade systems, Phys. Rev. B 67, 085316 (2003) 0163-1829 10.1103/PhysRevB.67.085316.
M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81, 1665 (2009) 0034-6861 10.1103/RevModPhys.81.1665.
P. C. Martin, E. Siggia, and H. Rose, Statistical dynamics of classical systems, Phys. Rev. A 8, 423 (1973) 0556-2791 10.1103/PhysRevA.8.423.
A. Lazarescu, T. Cossetto, G. Falasco, and M. Esposito, Large deviations and dynamical phase transitions in stochastic chemical networks, J. Chem. Phys. 151, 064117 (2019) 0021-9606 10.1063/1.5111110.
T. Cossetto, Ph.D. thesis, University of Luxembourg, 2020.
A. Greiner, W. Strittmatter, and J. Honerkamp, Numerical integration of stochastic differential equations, J. Stat. Phys. 51, 95 (1988) 0022-4715 10.1007/BF01015322.
D. T. Gillespie, Monte Carlo simulation of random walks with residence time dependent transition probability rates, J. Comput. Phys. 28, 395 (1978) 0021-9991 10.1016/0021-9991(78)90060-8.
D. F. Anderson, A modified next reaction method for simulating chemical systems with time dependent propensities and delays, J. Chem. Phys. 127, 214107 (2007) 0021-9606 10.1063/1.2799998.
