# Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments

Evstigneev M (2008)

PHYSICAL REVIEW E 78(1).

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The dynamics of a number of experimental systems can be described as thermally activated escape out of a metastable state over a potential barrier, whose height is being constantly reduced in time by an increasing external force. In such systems, one can distinguish two loading regimes: for slow loading, the distribution of the force values at which escape occurs is a monotonically decreasing function, while for fast loading, the escape-force distribution has a maximum at some nonzero force value. In this work, an approximate relation between the most probable escape force and the first two moments thereof is derived for fast loading, and the expression for the first two force moments vs loading rate is obtained for slow loading. Then, for a special but physically well-motivated functional form of the escape rate, the most probable escape force is found analytically as a function of the loading rate. The high accuracy of these expressions is confirmed by comparing them with numerical results for realistic parameter values.

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Evstigneev M. Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments.

*PHYSICAL REVIEW E*. 2008;78(1).Evstigneev, M. (2008). Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments.

*PHYSICAL REVIEW E*,*78*(1). doi:10.1103/PhysRevE.78.011118Evstigneev, M. (2008). Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments.

*PHYSICAL REVIEW E*78.Evstigneev, M., 2008. Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments.

*PHYSICAL REVIEW E*, 78(1). M. Evstigneev, “Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments”,

*PHYSICAL REVIEW E*, vol. 78, 2008. Evstigneev, M.: Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments. PHYSICAL REVIEW E. 78, (2008).

Evstigneev, Mykhaylo. “Statistics of forced thermally activated escape events out of a metastable state: Most probable escape force and escape-force moments”.

*PHYSICAL REVIEW E*78.1 (2008).
This data publication is cited in the following publications:

This publication cites the following data publications:

### 1 Citation in Europe PMC

Data provided by Europe PubMed Central.

Model accounting for the effects of pulling-device stiffness in the analyses of single-molecule force measurements.

Maitra A, Arya G.,

PMID: 20366455

Maitra A, Arya G.,

*Phys. Rev. Lett.*104(10), 2010PMID: 20366455

### 20 References

Data provided by Europe PubMed Central.

AUTHOR UNKNOWN, 1999

Unbinding process of adsorbed proteins under external stress studied by atomic force microscopy spectroscopy.

Gergely C, Voegel J, Schaaf P, Senger B, Maaloum M, Horber JK, Hemmerle J.,

PMID: 10984503

Gergely C, Voegel J, Schaaf P, Senger B, Maaloum M, Horber JK, Hemmerle J.,

*Proc. Natl. Acad. Sci. U.S.A.*97(20), 2000PMID: 10984503

Intrinsic Fluctuations in a Superconducting Ring Closed with a Josephson Junction

Kurkijärvi,

Kurkijärvi,

*Physical Review B*6(3), 1972
Experimental Evidence of the Néel-Brown Model of Magnetization Reversal

Wernsdorfer,

Wernsdorfer,

*Physical Review Letters*78(9), 1997
Thermal effects on atomic friction.

Sang Y, Dube M, Grant M.,

PMID: 11690274

Sang Y, Dube M, Grant M.,

*Phys. Rev. Lett.*87(17), 2001PMID: 11690274

Escape-field distribution for escape from a metastable potential well subject to a steadily increasing bias field.

Garg A.,

PMID: 9978526

Garg A.,

*Phys. Rev., B Condens. Matter*51(21), 1995PMID: 9978526

Reaction-rate theory: fifty years after Kramers

Hänggi,

Hänggi,

*Reviews of Modern Physics*62(2), 1990
Thermal activation-induced sweep-rate dependence of magnetic switching astroid

Sun,

Sun,

*Applied Physics Letters*78(25), 2001
Summation of power series by self-similar factor approximants

YUKALOV,

YUKALOV,

*Physica A Statistical Mechanics and its Applications*328(3-4), 2003
Interaction potential and hopping dynamics governing sliding friction.

Riedo E, Gnecco E, Bennewitz R, Meyer E, Brune H.,

PMID: 14525243

Riedo E, Gnecco E, Bennewitz R, Meyer E, Brune H.,

*Phys. Rev. Lett.*91(8), 2003PMID: 14525243

Beyond the conventional description of dynamic force spectroscopy of adhesion bonds.

Dudko OK, Filippov AE, Klafter J, Urbakh M.,

PMID: 13679588

Dudko OK, Filippov AE, Klafter J, Urbakh M.,

*Proc. Natl. Acad. Sci. U.S.A.*100(20), 2003PMID: 13679588

Brownian motion in a field of force and the diffusion model of chemical reactions

KRAMERS,

KRAMERS,

*Physica*7(4), 1940
On the LambertW function

Corless,

Corless,

*Advances in Computational Mathematics*5(1), 1996
Theoretical analysis of single-molecule force spectroscopy experiments: heterogeneity of chemical bonds.

Raible M, Evstigneev M, Bartels FW, Eckel R, Nguyen-Duong M, Merkel R, Ros R, Anselmetti D, Reimann P.,

PMID: 16513778

Raible M, Evstigneev M, Bartels FW, Eckel R, Nguyen-Duong M, Merkel R, Ros R, Anselmetti D, Reimann P.,

*Biophys. J.*90(11), 2006PMID: 16513778

Intrinsic rates and activation free energies from single-molecule pulling experiments.

Dudko OK, Hummer G, Szabo A.,

PMID: 16605793

Dudko OK, Hummer G, Szabo A.,

*Phys. Rev. Lett.*96(10), 2006PMID: 16605793

Force dependence of transition rates in atomic friction.

Evstigneev M, Schirmeisen A, Jansen L, Fuchs H, Reimann P.,

PMID: 17280262

Evstigneev M, Schirmeisen A, Jansen L, Fuchs H, Reimann P.,

*Phys. Rev. Lett.*97(24), 2006PMID: 17280262

Analyzing single-bond experiments: influence of the shape of the energy landscape and universal law between the width, depth, and force spectrum of the bond.

Husson J, Pincet F.,

PMID: 18352091

Husson J, Pincet F.,

*Phys Rev E Stat Nonlin Soft Matter Phys*77(2 Pt 2), 2008PMID: 18352091

Dynamic strength of molecular adhesion bonds.

Evans E, Ritchie K.,

PMID: 9083660

Evans E, Ritchie K.,

*Biophys. J.*72(4), 1997PMID: 9083660

Kinetics from nonequilibrium single-molecule pulling experiments.

Hummer G, Szabo A.,

PMID: 12829459

Hummer G, Szabo A.,

*Biophys. J.*85(1), 2003PMID: 12829459

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