随机控制和热力学第二定律

1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes Pub Date : 1900-01-01 DOI:10.1109/CDC.1978.268083

R. Brockett, J. Willems

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引用次数: 55

摘要

从随机控制理论的角度研究了热力学第二定律。我们发现我们感兴趣的反馈控制律是那些只依赖于平均值而不依赖于样本路径行为的律。我们得到一个准则，当满足该准则时，允许人们以这样一种方式将温度分配给随机系统，使卡诺循环成为最优控制问题的最优轨迹。熵也有定义，我们可以用温度的这个定义来证明能量均分定理。我们的公式允许人们以一种相当自然和完全精确的方式来处理不可逆性。

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Stochastic control and the second law of thermodynamics

The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.

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1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes

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