Control and Sensing in Thermally Fluctuating Systems

Ken Sekimoto

Yukawa Institute for Theoretical Physics,
Kyoto University, Kyoto 606-8502 Japan

Recently the author has explored with his colleagues the framework of energetics of fluctuating systems (called stochastic energetics). This framework was motivated by the recent development of nano-scale experiments and numerical simulation and then naturally urges us to reconsider apparently clear distinctions such as work {\it vs.} heat, signal {\it vs.} noise, system {\it vs.} its environment, or macroscopic {\it vs.} microscopic quantities.

In the present paper we will explore the control and sensing in the fluctuating systems, taking their energetics into account.

First we discuss the irreversibility and the cost related to external control and sensing. As concrete examples we will discuss microscopic Carnot cycles and its counterpart of an open environment with particle exchanges. Also we give a general consideration about the observation of thermodynamic functions.

Then we discuss automatic control of fluctuating systems surrounded by thermal and open environments. After a brief survey of automatic mechanisms of Feynman's ratchet and of B\"uttiker's model, we will explore the mechanisms with more accurate sensing and control, which will be relevant to the bio-molecular pumps and motors. Through concrete models we will show how a kind of self-reference is established within the system.

Designing and implementation of control and sensing within a fluctuating system seem to be of fundamental and conceptual interest, besides of practical and technical interest, and are related to the physics of computation and that of observation.