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Entropy production of a Brownian ellipsoid in the overdamped limit
KTH, School of Computer Science and Communication (CSC). Nordita. (Prof. Dr. Erik Aurell's Group)ORCID iD: 0000-0002-4384-8816
Department of Computational Biology and ACCESS Linnaeus Centre and Center for Quantum Materials, KTH–Royal Institute of Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden and Deptartments of Information and Computer Science and Applied Physics, Aalto University, Espoo, Finland.
Nordita, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden.
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.

Place, publisher, year, edition, pages
2016. Vol. 93, no 012132, 1-15 p.
Keyword [en]
Brownian motion, stochastic thermodynamics
National Category
Natural Sciences Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-207035DOI: 10.1103/PhysRevE.93.012132OAI: oai:DiVA.org:kth-207035DiVA: diva2:1095376
Note

QC 20170515

Available from: 2017-05-12 Created: 2017-05-12 Last updated: 2017-05-15Bibliographically approved
In thesis
1. Dynamics and Thermodynamics of Translational and Rotational Diffusion Processes Driven out of Equilibrium
Open this publication in new window or tab >>Dynamics and Thermodynamics of Translational and Rotational Diffusion Processes Driven out of Equilibrium
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
Translational and Rotational Diffusion Processes, Brownian
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-207039 (URN)978-91-7729-405-4 (ISBN)
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

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Publisher's full texthttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.012132

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