MEIBOHM, Jan Nicolas ; 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)
External co-authors :
no
Language :
English
Title :
Small-amplitude synchronization in driven Potts models
A. S. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Unified Approach to Nonlinear Science (Cambridge University Press, Cambridge, UK, 2001).
S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, The synchronization of chaotic systems, Phys. Rep. 366, 1 (2002) 0370-1573 10.1016/S0370-1573(02)00137-0.
J. A. Acebrón, L. L. Bonilla, C. J. P. Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77, 137 (2005) 0034-6861 10.1103/RevModPhys.77.137.
A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Synchronization in complex networks, Phys. Rep. 469, 93 (2008) 0370-1573 10.1016/j.physrep.2008.09.002.
M. Rosenblum and A. Pikovsky, Synchronization: From pendulum clocks to chaotic lasers and chemical oscillators, Contemp. Phys. 44, 401 (2003) 0010-7514 10.1080/00107510310001603129.
R. M. May, Limit cycles in predator-prey communities, Science 177, 900 (1972) 0036-8075 10.1126/science.177.4052.900.
C. S. Peskin, Mathematical Aspects of Heart Physiology (Courant Institute of Mathematical Sciences, New York, 1975), pp. 268-278.
D. C. Michaels, E. P. Matyas, and J. Jalife, Mechanisms of sinoatrial pacemaker synchronization: A new hypothesis, Circ. Res. 61, 704 (1987) 0009-7330 10.1161/01.RES.61.5.704.
M. E. Jewett and R. E. Kronauer, Refinement of limit cycle oscillator model of the effects of light on the human circadian pacemaker, J. Theor. Biol. 192, 455 (1998) 0022-5193 10.1006/jtbi.1998.0667.
J. Fell and N. Axmacher, The role of phase synchronization in memory processes, Nat. Rev. Neurosci. 12, 105 (2011) 1471-003X 10.1038/nrn2979.
A. F. Taylor, M. R. Tinsley, F. Wang, Z. Huang, and K. Showalter, Dynamical quorum sensing and synchronization in large populations of chemical oscillators, Science 323, 614 (2009) 0036-8075 10.1126/science.1166253.
L. Bello, M. Calvanese Strinati, E. G. Dalla Torre, and A. Pe'er, Persistent coherent beating in coupled parametric oscillators, Phys. Rev. Lett. 123, 083901 (2019) 0031-9007 10.1103/PhysRevLett.123.083901.
D. Chalkiadakis and J. Hizanidis, Dynamical properties of neuromorphic Josephson junctions, Phys. Rev. E 106, 044206 (2022) 2470-0045 10.1103/PhysRevE.106.044206.
R. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
R. B. Potts, Some generalized order-disorder transformations, in Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge University Press, Cambridge, UK, 1952), Vol. 48, pp. 106-109.
Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics Vol. 30 (Springer, Berlin, 1975), pp. 420-422.
S. H. Strogatz, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D 143, 1 (2000) 0167-2789 10.1016/S0167-2789(00)00094-4.
K. Wood, C. Van den Broeck, R. Kawai, and K. Lindenberg, Universality of synchrony: Critical behavior in a discrete model of stochastic phase-coupled oscillators, Phys. Rev. Lett. 96, 145701 (2006) 0031-9007 10.1103/PhysRevLett.96.145701.
T. Herpich, J. Thingna, and M. Esposito, Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions, Phys. Rev. X 8, 031056 (2018) 2160-3308 10.1103/PhysRevX.8.031056.
T. Herpich and M. Esposito, Universality in driven Potts models, Phys. Rev. E 99, 022135 (2019) 2470-0045 10.1103/PhysRevE.99.022135.
J. Meibohm and M. Esposito, companion paper, Minimum-dissipation principle for synchronized stochastic oscillators far from equilibrium, Phys. Rev. E 110, L042102 (2024) 10.1103/PhysRevE.110.L042102.
I. Prigogine, Introduction to Thermodynamics of Irreversible Processes (Charles C Thomas, Springfield, IL, 1955).
B. Barbara, M. F. Rossignol, and P. Bak, First-order transitions and tricritical points in (Equation presented): A realisation of the three-state Potts model, J. Phys. C 11, L183 (1978) 0022-3719 10.1088/0022-3719/11/5/007.
L. D. Roelofs, A. R. Kortan, T. L. Einstein, and R. L. Park, Critical exponents of a four-state Potts chemisorbed overlayer: (Equation presented)((Equation presented)) oxygen on Ni(111), Phys. Rev. Lett. 46, 1465 (1981) 0031-9007 10.1103/PhysRevLett.46.1465.
M. Schick, The classification of order-disorder transitions on surfaces, Prog. Surf. Sci. 11, 245 (1981) 0079-6816 10.1016/0079-6816(81)90002-2.
B. K. Das and R. B. Griffiths, A search for multicritical points in liquid mixtures: The shield region and the three-state Potts point, J. Chem. Phys. 70, 5555 (1979) 0021-9606 10.1063/1.437429.
M. Tsoi, A. G. M. Jansen, J. Bass, W.-C. Chiang, V. Tsoi, and P. Wyder, Generation and detection of phase-coherent current-driven magnons in magnetic multilayers, Nature (London) 406, 46 (2000) 0028-0836 10.1038/35017512.
F. B. Mancoff, N. D. Rizzo, B. N. Engel, and S. Tehrani, Phase-locking in double-point-contact spin-transfer devices, Nature (London) 437, 393 (2005) 0028-0836 10.1038/nature04036.
A. A. Awad, A. Houshang, M. Dvornik, and R. K. Dumas, Long-range mutual synchronization of spin Hall nano-oscillators, Nat. Phys. 13, 292 (2017) 1745-2473 10.1038/nphys3927.
D. Mukamel, M. E. Fisher, and E. Domany, Magnetization of cubic ferromagnets and the three-component Potts model, Phys. Rev. Lett. 37, 565 (1976) 0031-9007 10.1103/PhysRevLett.37.565.
E. Domany, M. Schick, and J. S. Walker, Classification of order-disorder transitions in common adsorbed systems: Realization of the four-state Potts model, Phys. Rev. Lett. 38, 1148 (1977) 0031-9007 10.1103/PhysRevLett.38.1148.
J. C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater. 159, L1 (1996) 0304-8853 10.1016/0304-8853(96)00062-5.
L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B 54, 9353 (1996) 0163-1829 10.1103/PhysRevB.54.9353.
U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012) 0034-4885 10.1088/0034-4885/75/12/126001.
C. Van den Broeck and M. Esposito, Ensemble and trajectory thermodynamics: A brief introduction, Physica A 418, 6 (2015) 0378-4371 10.1016/j.physa.2014.04.035.
L. Peliti and S. Pigolotti, Stochastic Thermodynamics: An Introduction (Princeton University Press, Princeton, NJ, 2021).
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 2007).
C. W. Gardiner, Handbook of Stochastic Methods: For the Natural and Social Sciences (Springer, Berlin, 2009).
O. Perron, Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus, Math. Ann. 64, 1 (1907) 0025-5831 10.1007/BF01449880.
G. Frobenius, Über Matrizen aus nicht negativen Elementen, Preuss. Akad. Wiss. Berlin, 456 (1912).
T. Herpich, T. Cossetto, G. Falasco, and M. Esposito, Stochastic thermodynamics of all-to-all interacting many-body systems, New J. Phys. 22, 063005 (2020) 1367-2630 10.1088/1367-2630/ab882f.
We note that the used term "Arrhenius rate" refers to the exponential form of the transition rates in Eq. (26) and not to its dependence on the initial and final energies.
G. Falasco and M. Esposito, Macroscopic stochastic thermodynamics, arXiv:2307.12406.
The additive form of the (Equation presented) is a direct consequence of the coarse graining (Equation presented), see e.g. the discussion in U. Seifert, From stochastic thermodynamics to thermodynamic inference, Annu. Rev. Condens. Matter Phys. 10, 171 (2019) 1947-5454 10.1146/annurev-conmatphys-031218-013554.
M. Baiesi and G. Falasco, Inflow rate, a time-symmetric observable obeying fluctuation relations, Phys. Rev. E 92, 042162 (2015) 1539-3755 10.1103/PhysRevE.92.042162.
E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, UK, 2002).
M. Golubitsky, I. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory (Springer, New York, 1988), Vol. II.
J. D. Crawford and E. Knobloch, Symmetry and symmetry-breaking bifurcations in fluid dynamics, Annu. Rev. Fluid Mech. 23, 341 (1991) 0066-4189 10.1146/annurev.fl.23.010191.002013.
M. Golubitsky and I. Stewart, The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space, (Springer, Berlin, 2003), Vol. 200.
P. J. Davis, Circulant Matrices (Wiley, New York, 1979), Vol. 120.
J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences Vol. 42 (Springer, Berlin, 1983).
J. D. Crawford, Introduction to bifurcation theory, Rev. Mod. Phys. 63, 991 (1991) 0034-6861 10.1103/RevModPhys.63.991.
C. Elphick, E. Tirapegui, M. E. Brachet, P. Coullet, and G. Iooss, A simple global characterization for normal forms of singular vector fields, Physica D 29, 95 (1987) 0167-2789 10.1016/0167-2789(87)90049-2.
J. Sherman and W. J. Morrison, Adjustment of an inverse matrix corresponding to a change in one element of a given matrix, Ann. Math. Stat. 21, 124 (1950) 0003-4851 10.1214/aoms/1177729893.
M. Brookes, The Matrix Reference Manual (2020), http://www.ee.imperial.ac.uk/hp/staff/dmb/matrix/intro.html.
J. R. Bunch, C. P. Nielsen, and D. C. Sorensen, Rank-one modification of the symmetric eigenproblem, Numer. Math. 31, 31 (1978) 0029-599X 10.1007/BF01396012.
R. C. Thompson, The behavior of eigenvalues and singular values under perturbations of restricted rank, Linear Algebra Appl. 13, 69 (1976) 0024-3795 10.1016/0024-3795(76)90044-6.
J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford University Press, Clarendon, 1965), Vol. 662.
D. Zhang, Y. Cao, Q. Ouyang, and Y. Tu, The energy cost and optimal design for synchronization of coupled molecular oscillators, Nat. Phys. 16, 95 (2020) 1745-2473 10.1038/s41567-019-0701-7.
B. Nguyen, U. Seifert, and A. C. Barato, Phase transition in thermodynamically consistent biochemical oscillators, J. Chem. Phys. 149, 045101 (2018) 10.1063/1.5032104.
I. Prigogine and P. Glansdorff, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley-Interscience, 1971).
D. Kondepudi and I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures (John Wiley & Sons, New York, 2014).
D. Daems and G. Nicolis, Entropy production and phase space volume contraction, Phys. Rev. E 59, 4000 (1999) 1063-651X 10.1103/PhysRevE.59.4000.
D. Ruelle, Positivity of entropy production in nonequilibrium statistical mechanics, J. Stat. Phys. 85, 1 (1996) 0022-4715 10.1007/BF02175553.
D. J. Searles and D. J. Evans, The fluctuation theorem and Green-Kubo relations, J. Chem. Phys. 112, 9727 (2000) 0021-9606 10.1063/1.481610.
D. J Evans and G. P Morriss, Statistical Mechanics of Nonequilbrium Liquids, 2nd ed. (Cambridge University Press, Cambridge, 2007).
D. T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys. 22, 403 (1976) 0021-9991 10.1016/0021-9991(76)90041-3.
P. Gaspard, Stochastic approach to entropy production in chemical chaos, Chaos 30, 113103 (2020) 10.1063/5.0025350.
P. Gaspard, Trace formula for noisy flows, J. Stat. Phys. 106, 57 (2002) 0022-4715 10.1023/A:1013167928166.
P. Gaspard, The correlation time of mesoscopic chemical clocks, J. Chem. Phys. 117, 8905 (2002) 0021-9606 10.1063/1.1513461.
A. C. Barato and U. Seifert, Coherence of biochemical oscillations is bounded by driving force and network topology, Phys. Rev. E 95, 062409 (2017) 2470-0045 10.1103/PhysRevE.95.062409.
A. Manacorda and É. Fodor, Pulsating with discrete symmetry, arXiv:2310.14370.