Tham khảo tài liệu 'understanding non-equilibrium thermodynamics - springer 2008 episode 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Keizer s Theory Fluctuations in Non-Equilibrium Steady States 291 where vi is the force conjugated to fi. As a consequence any intensive variable like for instance the temperature T conjugated to the internal energy U through 1 T dSK dU will be given by 1 . dvi Tq - f dữ 1 T This result shares some features with EIT as it exhibits the property that the temperature is not equal to the local equilibrium temperature Teq but contains additional terms depending on the fluxes see Box . An alternative expression of the generalized entropy more explicit in the fluctuations and based on is Sk x f r Seq x -1 k - 2 xixj v 1 - v-q ij where x0 U corresponds to the internal energy. It is directly inferred from that the temperature can be cast in the form 1 Tq - kB E Xi vTo1 - This result is important as it points out that non-equilibrium temperature the same reasoning remains valid for the pressure or the chemical potential is not identical to the local equilibrium one but is related to it through the difference of the non-equilibrium and equilibrium correlation function of the fluctuations. A spontaneous variation of the extensive variables xi will lead to a rate of change of entropy given by dSK _ dxi n-icQt dT iq 1L63 Using the property that for small deviations with respect to the steady state d2 s ss h - ss dxidxj xj - XjS can be written as J2Sk ỘÍ - ộiq xi - xss i and after differentiation with respect to time Sk 2 ội - ộin t 0. 292 11 Mesoscopic Thermodynamic Descriptions Rearranging one obtains dx dxi - 1L67 The left-hand side of inequality refers to the instantaneous values of the intensive variables whereas the right-hand side involves their average values in the steady state but in virtue of the left-hand side is also the rate of change of entropy so that finally S - i which was called by Keizer a generalized Clausius inequality because it generalizes Clausius inequality ĨRdS dt dQ
