Linear stochastic system with delay: energy balance and entropy production.
We study the energy balance in a linear stochastic dynamics with delay under the impact of an external periodic force. The linearity of the model, in combination with a response function method, enables us to perform detailed analytic calculations of each term in the energy balance equation. From this, we discuss thermodynamics and entropy production rate sigma . With use of the delay time tau and strength of the external force A0 , sigma is simply expressed as sigma=sigma_{D,1}(tau)+A_{0};{2}eta(tau) , with both sigma_{D,1}(tau) and eta(tau) positive definite. We thus conclude that even when there is no external force (A_{0}=0) , the entropy production rate sigma=sigma_{D,1}(tau) is positive, meaning that the delay force produces work, which is dissipated into a reservoir. Numerical experiments are performed to confirm theoretical results.
Munakata
Toyonori
T
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Iwama
Shinpei
S
Kimizuka
Makoto
M