Kawai R, Parrondo J M R, Van den Broeck C
Department of Physics, University of Alabama at Birmingham, Birmingham, AL 35294, USA.
Phys Rev Lett. 2007 Feb 23;98(8):080602. doi: 10.1103/PhysRevLett.98.080602. Epub 2007 Feb 22.
We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by <W{diss}> =W-DeltaF=kTD(rho||rho[over ])=kT<ln(rho/rho[over ])>, where rho and rho[over ] are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process. D(rho||rho[over ]) is the relative entropy of rho versus rho[over ]. This result also implies general inequalities, which are significantly more accurate than the second law and include, as a special case, the celebrated Landauer principle on the dissipation involved in irreversible computations.
我们通过对功定理的细化表明，在两个正则平衡态之间的转变中，将哈密顿系统任意地扰动到远离平衡态时，平均耗散量精确地由<W{diss}> =W - ΔF = kT D(ρ||ρ̅) = kT <ln(ρ/ρ̅)>给出，其中ρ和ρ̅是在正向和反向过程中，在相同的中间但任意时刻测量的系统相空间密度。D(ρ||ρ̅)是ρ相对于ρ̅的相对熵。这个结果还意味着一些一般不等式，它们比第二定律精确得多，并且作为一个特殊情况，包含了关于不可逆计算中所涉及耗散的著名的兰道尔原理。
