Entropic Stochastic Resonance

📝 Abstract

We present a novel scheme for the appearance of Stochastic Resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. This Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single-molecules and nano-devices.

💡 Analysis

We present a novel scheme for the appearance of Stochastic Resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. This Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single-molecules and nano-devices.

📄 Content

arXiv:0807.2558v1 [cond-mat.stat-mech] 16 Jul 2008 En tropi Sto

hasti Resonan e P .S. Burada, 1 G. S hmid, 1 D. Reguera, 2 M.H. V ainstein, 2 J.M. Rubi, 2 and P . Hänggi 1 1 Institut für Physik, Universität A ugsbur g, Universitätsstr. 1, D-86135 A ugsbur g, Germany 2 Dep artament de Físi a F onamental, F a ultat de Físi a, Universidad de Bar

elona, Diagonal 647, E-08028 Bar

elona, Sp ain (Dated: No v em b er 1, 2018) W e presen t a no v el s heme for the app earan e of Sto

hasti Resonan e when the dynami s of a Bro wnian parti le tak es pla e in a onned medium. The presen e of unev en b oundaries, giving rise to an en tropi on tribution to the p oten tial, ma y up on appli ation of a p erio di driving for e result in an in rease of the sp e tral ampli ation at an optim um v alue of the am bien t noise lev el. This Entr opi Sto hasti R esonan e (ESR),

hara teristi of small-s ale systems, ma y onstitute a useful me hanism for the manipulation and on trol of single-mole ules and nano-devi es. P A CS n um b ers: 02.50.Ey , 05.40.-a, 05.10.Gg Sto hasti R esonan e (SR) des rib es the oun terin tu- itiv e phenomenon where an appropriate dose of noise is not harmful for the dete tion or transdu tion of an in- oming, generally w eak signal, but rather of onstru tiv e use in the sense that a w eak signal b e omes amplied up on harv esting the am bien t noise in metastable, non- linear systems [1℄. Sin e its rst dis o v ery in the early eigh ties SR has b een observ ed in a great v ariet y of sys- tems p ertaining to dieren t dis iplines su h as ph ysi s,

hemistry , engineering, biology and biomedi al s ien es [1, 2, 3 , 4, 5, 6 , 7, 8, 9 , 10 ℄. The list of mo dels and ap- pli ations is still gro wing. In parti ular, SR has found widespread in terests and appli ations within biologi al ph ysi s. The resear h on SR has primarily b een fo used on sys- tems with purely energeti p oten tials. Ho w ev er, in sit- uations frequen tly found in soft ondensed matter and biologi al systems, parti les mo v e in onstrained regions su h as small a vities, p ores or

hannels whose pres- en e and shap e pla y an imp ortan t role for the SR- dynami s [10 ℄, sometimes ev en more imp ortan t than the w ell-studied ase of energeti barriers in su h systems [11 , 12 , 13 , 14 ℄. In this w ork, w e demonstrate that ir- regularities in the form of onning, urv ed b oundaries, b eing mo deled via an en tropi p oten tial, an ause noise- assisted, resonan t-lik e b eha viors in the system under on- sideration. Connemen t, an inheren t prop ert y of small- s ale systems, an th us onstitute an imp ortan t sour e of noise-indu ed resonan t ee ts with in teresting appli- ations in the design and on trol of these systems. The phenomenon of SR is ro oted on a sto

hasti syn-

hronization b et w een noise-indu ed hopping ev en ts and the rh ythm of the externally applied signal, that tak en alone is not su ien t for the system to o v er ome a p o- ten tial barrier. In the rst pla e, noise enables system transitions and it is in fa t resp onsible for the observ ed signal ampli ation and the emergen e of ertain degree of order. In the earliest and basi manifestation of SR, the syn hronization of the random swit hes of a Bro wn- ian parti le with a p erio di driving for e w ere observ ed for a bistable p oten tial. Moreo v er, p oten tials of this t yp e are not only found in systems with energy barriers, as ⃗G ⃗F(t) Lx Ly b x y FIG. 1: S hemati illustration of the t w o-dimensional stru - ture onning the motion of the Bro wnian parti les. The symmetri stru ture is dened b y a quarti double w ell fun - tion, f. Eq. (2), in v olving the geometri al parameters Lx , Ly and b. Bro wnian parti les are driv en b y a sin usoidal for e ⃗F(t) along the longitudinal dire tion and a onstan t for e ⃗G in the transv ersal dire tion. they ma y also arise due to the inuen e of en tropi on- strain ts. P arti les diusing freely in a onned medium su h as the one depi ted in Fig. 1 ma y giv e rise to an a tiv ation regime when a onstan t for e ⃗G in the trans- v erse dire tion is imp osed. W e will sho w that the om- bination of for ing and the presen e of en tropi ee ts deriving from the onnemen t and the irregularit y of the b oundaries giv e rise to an ee tiv e bistable p oten tial that exhibits the signatures of Sto

hasti Resonan e. The dynami s of a parti le in a onstrained geometry sub je ted to a sin usoidal os illating for e F(t) along the axis of the stru ture and to a onstan t for e G in the transv ersal dire tion an b e des rib ed b y means of the Langevin equation, written in the o v erdamp ed limit as γ d⃗r dt = −G⃗ey −F(t) ⃗ex + p γ kBT ⃗ξ(t) , (1) where ⃗r denotes the p osition of the parti le, γ is the fri tion o e ien t, ⃗ex and ⃗ey the unit v e tors along the x and y -dire tions, resp e tiv ely , and ⃗ξ(t) is a Gaussian white noise with zero me

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