### Abstract

In carrying a Brownian particle by means of an external force in one dimension from a place to another in a finite time lapse, we consider controlling the force using a feedback loop to minimize an evaluation functional. The evaluation functional contains the average of the work done to the particle by the force and two terms involving control parameters. One is a term proportional to the mean squared force, while the other is a term proportional to the mean squared distance between the final particle position and the destination. Solving differential equations numerically, we calculate the average work under optimal control for various values of control parameters and find the calculated values bounded from below. The average work is also shown to be larger as we utilize less information on the state of the particle in the feedback control by decreasing the number of observed variables and by increasing the noise amplitude in the observation.

Original language | English |
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Article number | 074007 |

Journal | Journal of the Physical Society of Japan |

Volume | 78 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2009 Jul |

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### Keywords

- Kalman filter
- Mutual information
- Optimal protocol
- Stochastic energetics
- The second law

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**One-dimensional shift of a brownian particle under the feedback control.** / Suzuki, Hiroyuki; Fujitani, Youhei.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 78, no. 7, 074007. https://doi.org/10.1143/JPSJ.78.074007

}

TY - JOUR

T1 - One-dimensional shift of a brownian particle under the feedback control

AU - Suzuki, Hiroyuki

AU - Fujitani, Youhei

PY - 2009/7

Y1 - 2009/7

N2 - In carrying a Brownian particle by means of an external force in one dimension from a place to another in a finite time lapse, we consider controlling the force using a feedback loop to minimize an evaluation functional. The evaluation functional contains the average of the work done to the particle by the force and two terms involving control parameters. One is a term proportional to the mean squared force, while the other is a term proportional to the mean squared distance between the final particle position and the destination. Solving differential equations numerically, we calculate the average work under optimal control for various values of control parameters and find the calculated values bounded from below. The average work is also shown to be larger as we utilize less information on the state of the particle in the feedback control by decreasing the number of observed variables and by increasing the noise amplitude in the observation.

AB - In carrying a Brownian particle by means of an external force in one dimension from a place to another in a finite time lapse, we consider controlling the force using a feedback loop to minimize an evaluation functional. The evaluation functional contains the average of the work done to the particle by the force and two terms involving control parameters. One is a term proportional to the mean squared force, while the other is a term proportional to the mean squared distance between the final particle position and the destination. Solving differential equations numerically, we calculate the average work under optimal control for various values of control parameters and find the calculated values bounded from below. The average work is also shown to be larger as we utilize less information on the state of the particle in the feedback control by decreasing the number of observed variables and by increasing the noise amplitude in the observation.

KW - Kalman filter

KW - Mutual information

KW - Optimal protocol

KW - Stochastic energetics

KW - The second law

UR - http://www.scopus.com/inward/record.url?scp=67650799946&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650799946&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.78.074007

DO - 10.1143/JPSJ.78.074007

M3 - Article

VL - 78

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 7

M1 - 074007

ER -