Abstract
In the context of non-equilibrium statistical physics, the entropy production rate is an important concept to describe how far a specific state of a system is from its equilibrium state. In this paper, we establish a central limit theorem and a moderate deviation principle for the entropy production rate of d-dimensional Ornstein–Uhlenbeck processes, by the techniques of functional inequalities such as Poincaré inequality and log-Sobolev inequality. As an application, we obtain a law of iterated logarithm for the entropy production rate.
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Acknowledgments
The authors would like to gratefully thank the two anonymous referees for valuable suggestions. R. Wang thanks the Faculty of Science and Technology, University of Macau, for inviting and supporting. He is supported by Natural Science Foundation of China 11301498, 11431014 and the Fundamental Research Funds for the Central Universities WK0010000048. L. Xu is supported by the grant SRG2013-00064-FST and Science and Technology Development Fund, Macao S.A.R FDCT 049/2014/A1. Both of the authors are supported by the research Project RDAO/RTO/0386-SF/2014.
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Wang, R., Xu, L. Asymptotics of the Entropy Production Rate for d-Dimensional Ornstein–Uhlenbeck Processes. J Stat Phys 160, 1336–1353 (2015). https://doi.org/10.1007/s10955-015-1295-9
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DOI: https://doi.org/10.1007/s10955-015-1295-9
Keywords
- Functional inequality
- Ornstein–Uhlenbeck process
- Central limit theorem
- Moderate deviation principle
- Law of iterated logarithm
- Entropy production rate