Reciprocal Relations in Irreversible Processes. II. Export

@article{citeulike:1626400, abstract = {A general reciprocal relation; applicable to transport processes such as the conduction of heat and electricity; and diffusion; is derived from the assumption of microscopic reversibility. In the derivation; certain average products of fluctuations are considered. As a consequence of the general relation S = k  log W between entropy and probability; different (coupled) irreversible processes must be compared in terms of entropy changes. If the displacement from thermodynamic equilibrium is described by a set of variables α 1 ;⋯;α n ; and the relations between the rates α̇ 1 ;⋯;α̇ n and the "forces" ∂ S / d α 1 ;⋯;∂ S / d α n are linear; there exists a quadratic dissipation-function; 2Φ(α̇;α̇)≡Σρ j α̇ ij α̇ i = dS / dt = S ̇(α;α̇)≡Σ(∂ S / d α j )α̇ j (denoting definition by ≡). The symmetry conditions demanded by microscopic reversibility are equivalent to the variation-principle S ̇(α;α̇)-Φ(α̇;α̇)=maximum; which determines α̇ 1 ;⋯;α̇ n for prescribed α 1 ;⋯;α n . The dissipation-function has a statistical significance similar to that of the entropy. External magnetic fields; and also Coriolis forces; destroy the symmetry in past and future; reciprocal relations involving reversal of the field are formulated.}, author = {Onsager, Lars}, citeulike-article-id = {1626400}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRev.38.2265}, citeulike-linkout-1 = {http://link.aps.org/abstract/PR/v38/i12/p2265_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/PR/v38/i12/p2265_1}, day = {15}, doi = {10.1103/PhysRev.38.2265}, journal = {Physical Review}, keywords = {irreversible, thermodynamics}, month = {December}, number = {12}, pages = {2265+}, posted-at = {2009-01-14 16:52:55}, priority = {2}, publisher = {American Physical Society}, title = {Reciprocal Relations in Irreversible Processes. II.}, url = {http://dx.doi.org/10.1103/PhysRev.38.2265}, volume = {38}, year = {1931} }

TY - JOUR ID - citeulike:1626400 L3 - citeulike-article-id:1626400 N2 - A general reciprocal relation; applicable to transport processes such as the conduction of heat and electricity; and diffusion; is derived from the assumption of microscopic reversibility. In the derivation; certain average products of fluctuations are considered. As a consequence of the general relation S = k  log W between entropy and probability; different (coupled) irreversible processes must be compared in terms of entropy changes. If the displacement from thermodynamic equilibrium is described by a set of variables α 1 ;⋯;α n ; and the relations between the rates α̇ 1 ;⋯;α̇ n and the "forces" ∂ S / d α 1 ;⋯;∂ S / d α n are linear; there exists a quadratic dissipation-function; 2Φ(α̇;α̇)≡Σρ j α̇ ij α̇ i = dS / dt = S ̇(α;α̇)≡Σ(∂ S / d α j )α̇ j (denoting definition by ≡). The symmetry conditions demanded by microscopic reversibility are equivalent to the variation-principle S ̇(α;α̇)-Φ(α̇;α̇)=maximum; which determines α̇ 1 ;⋯;α̇ n for prescribed α 1 ;⋯;α n . The dissipation-function has a statistical significance similar to that of the entropy. External magnetic fields; and also Coriolis forces; destroy the symmetry in past and future; reciprocal relations involving reversal of the field are formulated. IS - 12 JF - Physical Review TI - Reciprocal Relations in Irreversible Processes. II. PB - American Physical Society VL - 38 SP - 2265 KW - irreversible KW - thermodynamics AU - Onsager, Lars PY - 1931/12/15/ UR - http://dx.doi.org/10.1103/PhysRev.38.2265 ER -