Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 457, Issue 2011, Pages 1645-1655Publisher
ROYAL SOC
DOI: 10.1098/rspa.2001.0811
Keywords
Brownian motion; entropy-production rate; fluctuation-dissipation relation; reversibility; stochastic macromolecular mechanics; sweeping
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We prove the equivalence among symmetricity, time reversibility and zero entropy production of the stationary solutions of linear stochastic differential equations. A sufficient and necessary reversibility condition expressed in terms of the coefficients of the equations is given. The existence of a linear stationary irreversible process is established. Concerning reversibility, we show that there is a contradistinction between any one-dimensional stationary Gaussian process and a stationary Gaussian process of dimension n > 1. A concrete criterion for differentiating stationarity and sweeping behaviour is also obtained. The mathematical result is a natural generalization of Einstein's fluctuation-dissipation relation, and provides a rigorous basis for the isothermal irreversibility in a linear regime, which is the basis for applying Onsager's theory to macromolecules in aqueous solution.
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