Mathematical formalism for isothermal linear irreversibility

Authors
Citation
H. Qian, Mathematical formalism for isothermal linear irreversibility, P ROY SOC A, 457(2011), 2001, pp. 1645-1655
Citations number
24
Categorie Soggetti
Multidisciplinary
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
ISSN journal
13645021 → ACNP
Volume
457
Issue
2011
Year of publication
2001
Pages
1645 - 1655
Database
ISI
SICI code
1364-5021(20010708)457:2011<1645:MFFILI>2.0.ZU;2-W
Abstract
We prove the equivalence among symmetricity, time reversibility and zero en tropy production of the stationary solutions of linear stochastic different ial 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 reversib ility, we show that there is a contradistinction between any one-dimensiona l stationary Gaussian process and a stationary Gaussian process of dimensio n n > 1. A concrete criterion for differentiating stationarity and sweeping behaviour is also obtained. The mathematical result is a natural generaliz ation of Einstein's fluctuation-dissipation relation, and provides a rigoro us basis for the isothermal irreversibility in a linear regime, which is th e basis for applying Onsager's theory to macromolecules in aqueous solution .