Abstract
Transport in confined structures of varying geometry has become the subject of growing attention in recent years since such structures are ubiquitous in biology and technology. In analyzing transport in systems of this type, the notion of entropy potentials is widely used. Entropy potentials naturally arise in one-dimensional description of equilibrium distributions in multidimensional confined structures. However, their application to transport problems requires some caution. In this article we discuss such applications and summarize the results of recent studies exploring the limits of applicability. We also consider an example of a transport problem in a system of varying geometry, where the conventional approach is inapplicable since the geometry changes abruptly. In addition, we demonstrate how the entropy potential can be used to analyze optimal transport through a three-dimensional cosine-shaped channel.
Similar content being viewed by others
References
M. Colombini, J. Membrane Biol. 111, 103 (1989)
T.K. Rostovtseva, S.M. Bezrukov, BBA-Biomembranes 1818, 1526 (2012)
R. Ujwal, D. Cascio, J.P. Colletier, S. Faham, J. Zhang, L. Toro, P.P. Ping, J. Abramson, Proc. Natl. Acad. Sci. USA 105, 17742 (2008)
S.Y. Noskov, T.K. Rostovtseva, S.M. Bezrukov, Biochemistry-Us 52, 9246 (2013)
A.M. Berezhkovskii, M.A. Pustovoit, S.M. Bezrukov, Phys. Rev. E 80, 020904 (2009)
S.M. Bezrukov, A.M. Berezhkovskii, A. Szabo, J. Chem. Phys. 127, 115101 (2007)
A.M. Berezhkovskii, S.M. Bezrukov, Chem. Phys. 319, 342 (2005)
A.M. Berezhkovskii, S.M. Bezrukov, Biophys. J. 88, L17 (2005)
A.M. Berezhkovskii, M.A. Pustovoit, S.M. Bezrukov, J. Chem. Phys. 119, 3943 (2003)
A.M. Berezhkovskii, M.A. Pustovoit, S.M. Bezrukov, J. Chem. Phys. 116, 9952 (2002)
S.M. Bezrukov, A.M. Berezhkovskii, M.A. Pustovoit, A. Szabo, J. Chem. Phys. 113, 8206 (2000)
A.M. Berezhkovskii, G. Hummer, S.M. Bezrukov, Phys. Rev. Lett. 97, 020601 (2006)
M.H. Jacobs, Diffusion Processes (Springer, New York, 1967)
H. Nikaido, Microbiol Mol. Biol. R 67, 593 (2003)
R. Zwanzig, J. Phys. Chem-Us 96, 3926 (1992)
D. Reguera, J.M. Rubi, Phys. Rev. E 64, 061106 (2001)
P. Kalinay, J.K. Percus, Phys. Rev. E 72, 061203 (2005)
P. Kalinay, J.K. Percus, Phys. Rev. E 74, 041203 (2006)
P. Kalinay, J.K. Percus, Phys. Rev. E 78, 021103 (2008)
P. Kalinay, J.K. Percus, Phys. Rev. E 82, 031143 (2010)
P. Kalinay, Phys. Rev. E 80, 031106 (2009)
S. Martens, G. Schmid, L. Schimansky-Geier, P. Hanggi 21, 047518 (2011)
S. Martens, G. Schmid, L. Schimansky-Geier, P. Hanggi, Phys. Rev. E 83, 051135 (2011)
A. Berezhkovskii, A. Szabo, J. Chem. Phys. 135, 074108 (2011)
R.M. Bradley, Phys. Rev. E 80, 061142 (2009)
L. Dagdug, I. Pineda, J. Chem. Phys. 137, 024107 (2012)
A.M. Berezhkovskii, M.A. Pustovoit, S.M. Bezrukov, J. Chem. Phys. 126, 134706 (2007)
L. Dagdug, M.V. Vazquez, A.M. Berezhkovskii, S.M. Bezrukov, J. Chem. Phys. 133, 034707 (2010)
S. Lifson, J.L. Jackson, J. Chem. Phys. 36, 2410 (1962)
P.S. Burada, G. Schmid, D. Reguera, J.M. Rubi, P. Hanggi, Phys. Rev. E 75, 051111 (2007)
P.S. Burada, G. Schmid, P. Talkner, P. Hanggi, D. Reguera, J.M. Rubi, Biosystems 93, 16 (2008)
A.M. Berezhkovskii, A.V. Barzykin, V.Y. Zitserman, J. Chem. Phys. 131, 224110 (2009)
Y.A. Makhnovskii, A.M. Berezhkovskii, V.Y. Zitserman, J. Chem. Phys. 131, 104705 (2009)
A.M. Berezhkovskii, M.I. Monine, C.B. Muratov, S.Y. Shvartsman, J. Chem. Phys. 124, (2006)
T.L. Hill, Proc. Natl. Acad. Sci. USA 72, 4918 (1975)
H.C. Berg, E.M. Purcell, Biophys. J. 20, 193 (1977)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Berezhkovskii, A.M., Bezrukov, S.M. On the applicability of entropy potentials in transport problems. Eur. Phys. J. Spec. Top. 223, 3063–3077 (2014). https://doi.org/10.1140/epjst/e2014-02319-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2014-02319-3