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Resolution dependence of most probable pathways with state-dependent diffusivity (2402.01559v1)
Published 2 Feb 2024 in cond-mat.stat-mech, cond-mat.mes-hall, cond-mat.soft, and physics.chem-ph
Abstract: Recent experiments have probed the relative likelihoods of trajectories in stochastic systems by observing survival probabilities within a tube of radius $R$ in spacetime. We measure such probabilities here for a colloidal particle in a corrugated channel, corresponding to a bistable potential with state-dependent diffusivity. In contrast to previous findings for state-independent noise, we find that the most probable pathway changes qualitatively as the tube radius $R$ is altered. We explain this by computing the survival probabilities predicted by overdamped Langevin dynamics. At high enough resolution (small enough $R$), survival probabilities depend solely on diffusivity variations, independent of deterministic forces; finite $R$ corrections yield a generalization of the Onsager-Machlup action. As corollary, ratios of survival probabilities are singular as $R \to 0$, but become regular, and described by the classical Onsager-Machlup action, only in the special case of state-independent noise.
- M. I. Dykman, P. V. E. McClintock, V. N. Smelyanski, N. D. Stein, and N. G. Stocks, “Optimal paths and the prehistory problem for large fluctuations in noise-driven systems,” Physical Review Letters 68, 2718–2721 (1992).
- D G Luchinsky, P V E McClintock, and M I Dykman, “Analogue studies of nonlinear systems,” Reports on Progress in Physics 61, 889–997 (1998).
- Weinan E, Weiqing Ren, and Eric Vanden-Eijnden, “String method for the study of rare events,” Physical Review B 66, 052301 (2002).
- Weiqing Ren, Eric Vanden-Eijnden, Paul Maragakis, and Weinan E, “Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide,” The Journal of Chemical Physics 123, 134109 (2005).
- Weinan E, Weiqing Ren, and Eric Vanden-Eijnden, “Transition pathways in complex systems: Reaction coordinates, isocommittor surfaces, and transition tubes,” Chemical Physics Letters 413, 242–247 (2005).
- H. B. Chan, M. I. Dykman, and C. Stambaugh, “Paths of Fluctuation Induced Switching,” Physical Review Letters 100 (2008), 10.1103/PhysRevLett.100.130602.
- Hiroshi Fujisaki, Motoyuki Shiga, and Akinori Kidera, “Onsager–Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways,” The Journal of Chemical Physics 132, 134101 (2010).
- Timo Schorlepp, Tobias Grafke, and Rainer Grauer, “Gel’fand-Yaglom type equations for calculating fluctuations around instantons in stochastic systems,” Journal of Physics A: Mathematical and Theoretical 54, 235003 (2021).
- A D Ventsel’ and M I Freidlin, “On small random perturbations of dynamical systems,” Russian Mathematical Surveys 25, 1–55 (1970).
- Ruslan Leontievich Stratonovich, “On the probability functional of diffusion processes,” Selected Trans. in Math. Stat. Prob 10, 273 (1971).
- Detlef Dürr and Alexander Bach, “The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process,” Communications in Mathematical Physics 60, 153–170 (1978).
- Y. Takahashi and S. Watanabe, “The probability functionals (Onsager-machlup functions) of diffusion processes,” in Stochastic Integrals, Vol. 851, edited by David Williams (Springer Berlin Heidelberg, Berlin, Heidelberg, 1981) pp. 433–463.
- W. Horsthemke and A. Bach, ‘‘Onsager-Machlup Function for one dimensional nonlinear diffusion processes,” Zeitschrift für Physik B Condensed Matter and Quanta 22, 189–192 (1975).
- Ofer Zeitouni, “On the Onsager-Machlup Functional of Diffusion Processes Around Non C2 Curves,” The Annals of Probability 17, 1037–1054 (1989).
- H. Ito, “Probabilistic Construction of Lagrangean of Diffusion Process and Its Application,” Progress of Theoretical Physics 59, 725–741 (1978).
- Takahiko Fujita and Shin-ichi Kotani, “The Onsager-Machlup function for diffusion processes,” Journal of Mathematics of Kyoto University 22, 115–130 (1982).
- Nobuyuki Ikeda and Shinzo Watanabe, Stochastic differential Equations and diffusion processes, 2nd ed., North-Holland mathematical Library No. 24 (North-Holland [u.a.], Amsterdam, 1989) oCLC: 20080337.
- Julian Kappler and Ronojoy Adhikari, ‘‘Stochastic action for tubes: Connecting path probabilities to measurement,” Physical Review Research 2 (2020), 10.1103/PhysRevResearch.2.023407.
- Jannes Gladrow, Ulrich F. Keyser, R. Adhikari, and Julian Kappler, “Experimental Measurement of Relative Path Probabilities and Stochastic Actions,” Physical Review X 11, 031022 (2021).
- Nico G. van Kampen, Stochastic processes in physics and chemistry, 3rd ed., North-Holland personal library (Elsevier, Amsterdam ; Boston, 2007) oCLC: ocm81453662.
- Gerhard Hummer, “Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations,” New Journal of Physics 7, 34–34 (2005).
- Felix Sedlmeier, Yann von Hansen, Liang Mengyu, Dominik Horinek, and Roland R. Netz, “Water Dynamics at Interfaces and Solutes: Disentangling Free Energy and Diffusivity Contributions,” Journal of Statistical Physics 145, 240–252 (2011).
- Alexander Berezhkovskii and Attila Szabo, “Time scale separation leads to position-dependent diffusion along a slow coordinate,” The Journal of Chemical Physics 135, 074108 (2011).
- Stefano Bo, Soon Hoe Lim, and Ralf Eichhorn, “Functionals in stochastic thermodynamics: how to interpret stochastic integrals,” Journal of Statistical Mechanics: Theory and Experiment 2019, 084005 (2019).
- T. J. Murphy and J. L. Aguirre, “Brownian Motion of N Interacting Particles. I. Extension of the Einstein Diffusion Relation to the N-Particle Case,” The Journal of Chemical Physics 57, 2098–2104 (1972).
- Gerald Wilemski, “On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion,” Journal of Statistical Physics 14, 153–169 (1976).
- Rajesh Singh and R. Adhikari, ‘‘Fluctuating hydrodynamics and the Brownian motion of an active colloid near a wall,” European Journal of Computational Mechanics 26, 78–97 (2017).
- Yongge Li, Ruoxing Mei, Yong Xu, JÃŒrgen Kurths, Jinqiao Duan, and Ralf Metzler, “Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity,” New Journal of Physics 22, 053016 (2020).
- Robert Graham, “Path integral formulation of general diffusion processes,” Zeitschrift für Physik B Condensed Matter and Quanta 26, 281–290 (1977).
- F. Langouche, D. Roekaerts, and E. Tirapegui, “Functional integral methods for stochastic fields,” Physica A: Statistical Mechanics and its Applications 95, 252–274 (1979).
- C. Wissel, “Manifolds of equivalent path integral solutions of the Fokker-Planck equation,” Zeitschrift für Physik B Condensed Matter and Quanta 35, 185–191 (1979).
- H. Dekker, “On the path integral for diffusion in curved spaces,” Physica A: Statistical Mechanics and its Applications 103, 586–596 (1980).
- Leticia F Cugliandolo, Vivien Lecomte, and Frédéric van Wijland, “Building a path-integral calculus: a covariant discretization approach,” Journal of Physics A: Mathematical and Theoretical 52, 50LT01 (2019).
- Julian Kappler, Michael E. Cates, and Ronojoy Adhikari, “Sojourn probabilities in tubes and pathwise irreversibility for itô processes,” .
- Thibaut Arnoulx De Pirey, Leticia F. Cugliandolo, Vivien Lecomte, and Frédéric Van Wijland, “Path integrals and stochastic calculus,” Advances in Physics 71, 1–85 (2023).
- Alice L. Thorneywork, Jannes Gladrow, Yujia Qing, Marc Rico-Pasto, Felix Ritort, Hagan Bayley, Anatoly B. Kolomeisky, and Ulrich F. Keyser, “Direct detection of molecular intermediates from first-passage times,” Science Advances 6, eaaz4642 (2020).
- P. Kalinay and J. K. Percus, “Projection of two-dimensional diffusion in a narrow channel onto the longitudinal dimension,” The Journal of Chemical Physics 122, 204701 (2005).
- Kevin D. Dorfman and Ehud Yariv, “Assessing corrections to the Fick–Jacobs equation,” The Journal of Chemical Physics 141, 044118 (2014).
- Xiang Yang, Chang Liu, Yunyun Li, Fabio Marchesoni, Peter Hänggi, and H. P. Zhang, “Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels,” Proceedings of the National Academy of Sciences 114, 9564–9569 (2017).
- Julian Kappler, “Cloning algorithm for measuring rare events from stochastic time series, https://github.com/juliankappler/cloning_algorithm,” .