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Mathematical Formalism for Isothermal Linear Irreversibility

Hong Qian
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Abstract

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 1-dimensional stationary Gaussian process and stationary Gaussian process of dimension $n>1$. A concrete criterion for differentiating stationarity and sweeping behavior 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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BibTeXRIS

Hong Qian. 2001-06-27. Mathematical Formalism for Isothermal Linear Irreversibility. https://doi.org/10.1098/rspa.2001.0811

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