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Dynamics and Thermodynamics of Translational and Rotational Diffusion Processes Driven out of Equilibrium
KTH, School of Computer Science and Communication (CSC). Nordita. (Prof. Dr. Erik Aurell's Group)ORCID iD: 0000-0002-4384-8816
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Diffusion processes play an important role in describing systems in many fields of science, as in physics, biology, finance and social science. One of the most famous examples of the diffusion process is the Brownian motion. 

 

At mesoscopic scale, the Brownian theory describes the very irregular and animated motion of a particle suspended in a fluid. In this thesis, the dynamics and thermodynamics of diffusion processes driven out of equilibrium, at mesoscopic scale, are investigated. 

 

For dynamics, the theory of Brownian motion for a particle which is able to rotate and translate in three dimensions is presented. 

Moreover, it is presented how to treat diffusion process on n-dimensional Riemann manifolds defining the Kolmogorov forward equation on such manifold.

 

For thermodynamics, this thesis describes how to define thermodynamics quantities at mesoscopic scale using the tools of Brownian theory. The theory

of stochastic energetics and how to compute entropy production along a trajectory are presented introducing the new field of stochastic thermodynamics.

Moreover, the "anomalous entropy production" is introduced. This anomaly in the entropy production arises when diffusion processes are driven out of equilibrium by space dependent temperature field. The presence of this term expresses the fallacy of the overdamped approximation in computing thermodynamic quantities. 

 

In the first part of the thesis the translational and rotational motion of an ellipsoidal particle in a heterogeneous thermal environment, with a space-dependent temperature field, is analyzed from the point of view of stochastic thermodynamics. 

 

In the final part of the thesis, the motion of a Brownian rigid body three-dimensional space in a homogeneous thermal environment under the presence of an external force field is analyzed, using multiscale method and homogenization. 

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. , 97 p.
Series
TRITA-CSC-A, ISSN 1653-5723 ; 2017:13
Keyword [en]
Translational and Rotational Diffusion Processes, Brownian
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-207039ISBN: 978-91-7729-405-4 (print)OAI: oai:DiVA.org:kth-207039DiVA: diva2:1095387
Public defence
2017-06-15, FD5, D5:3008,, 5th floor, Roslagstullsbacken 12, AlbaNova, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20170515

Available from: 2017-05-15 Created: 2017-05-12 Last updated: 2017-05-22Bibliographically approved
List of papers
1. Entropy production of a Brownian ellipsoid in the overdamped limit
Open this publication in new window or tab >>Entropy production of a Brownian ellipsoid in the overdamped limit
2016 (English)In: PHYSICAL REVIEW E, Vol. 93, no 012132, 1-15 p.Article in journal, Editorial material (Refereed) Published
Abstract [en]

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called “anomalous” contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the “anomalous” entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the “anomalous entropy” for prolate and oblate spheroids and for near-spherical Brownian particles.

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called “anomalous” contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the “anomalous” entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the “anomalous entropy” for prolate and oblate spheroids and for near-spherical Brownian particles.

Keyword
Brownian motion, stochastic thermodynamics
National Category
Natural Sciences Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-207035 (URN)10.1103/PhysRevE.93.012132 (DOI)
Note

QC 20170515

Available from: 2017-05-12 Created: 2017-05-12 Last updated: 2017-05-15Bibliographically approved
2. Diffusion of a Brownian ellipsoid in a force field
Open this publication in new window or tab >>Diffusion of a Brownian ellipsoid in a force field
Show others...
2016 (English)In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 114, no 3, 30005Article in journal (Refereed) Published
Abstract [en]

We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a "net" average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-190517 (URN)10.1209/0295-5075/114/30005 (DOI)000379522200005 ()2-s2.0-84975842477 (ScopusID)
Funder
Swedish Research Council, 621-2012-2982Swedish Research Council, 621-2013-3956
Note

QC 20160817

Available from: 2016-08-17 Created: 2016-08-12 Last updated: 2017-05-12Bibliographically approved
3. Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry
Open this publication in new window or tab >>Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry
2016 (English)In: PHYSICAL REVIEW E, ISSN 2470-0045, Vol. 93, no 6, 062147Article in journal (Refereed) Published
Abstract [en]

We consider coupled diffusions in n-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multiscale analysis. As an example, we consider coupled diffusions in three-dimensional space and on the group manifold SO(3) of proper rotations, generalizing results obtained by H. Brenner [J. Colloid Interface Sci. 80, 548 (1981)]. We show in detail how the analysis can be conveniently carried out using local charts and invariance arguments. As a further example, we consider coupled diffusions in two-dimensional complex space and on the group manifold SU(2). We show that although the local operators may be the same as for SO(3), due to the global nature of the solvability conditions the resulting diffusion will differ and generally be more isotropic.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-190673 (URN)10.1103/PhysRevE.93.062147 (DOI)000378875200005 ()2-s2.0-84977083523 (ScopusID)
Note

QC 20160816

Available from: 2016-08-16 Created: 2016-08-12 Last updated: 2017-05-12Bibliographically approved
4. Brownian motion of an ellipsoidal particle in a tilted periodic potential: long-term velocity and diffusion
Open this publication in new window or tab >>Brownian motion of an ellipsoidal particle in a tilted periodic potential: long-term velocity and diffusion
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider the overdamped diffusive motion of an ellipsoidal Brownian particle in a tilted periodic potential. Exact analytical expressions for the net drift and diffusion of the ellipsoid are derived for the cases that it is much smaller, comparable in size and much larger than the periodicity of the potential. Known results for spherical particles are recovered as special cases.

Keyword
Brownian motion, tilted periodic potential
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-207055 (URN)
Note

QC 20170515

Available from: 2017-05-15 Created: 2017-05-15 Last updated: 2017-05-15Bibliographically approved

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