Van Vliet Carolyne M
Department of Physics, University of Miami, PO Box 248046, Coral Gables, Florida 33124-0530, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051106. doi: 10.1103/PhysRevE.86.051106. Epub 2012 Nov 6.
Nonequilibrium processes require that the density operator of an interacting system with Hamiltonian H(t) = H(0)(t)+λV converges and produces entropy. Employing projection operators in the state space, the density operator is developed to all orders of perturbation and then resummed. In contrast to earlier treatments by Van Hove [Physica 21, 517 (1955)] and others [U. Fano, Rev. Mod. Phys. 29, 74 (1959); U. Fano, in Lectures on the Many-Body Problem, Vol 2, edited by E. R. Caniello (Academic Press, New York, 1964); R. Zwanzig, in Lectures in Theoretical Physics, Vol. III, edited by W. E. Britten, B. W. Downs, and J. Downs (Wiley Interscience, New York, 1961), pp. 116-141; K. M. Van Vliet, J. Math. Phys. 19, 1345 (1978); K. M. Van Vliet, Can. J. Phys. 56, 1206 (1978)], closed expressions are obtained. From these we establish the time-reversal symmetry property P(γ,t|γ',t') = Pγ',t'|γ,t), where the tilde refers to the time-reversed protocol; also a nonstationary Markovian master equation is derived. Time-reversal symmetry is then applied to thermostatted systems yielding the Crooks-Tasaki fluctuation theorem (FT) and the quantum Jarzynski work-energy theorem, as well as the general entropy FT. The quantum mechanical concepts of work and entropy are discussed in detail. Finally, we present a nonequilibrium extension of Mazo's lemma of linear response theory, obtaining some applications via this alternate route.
非平衡过程要求具有哈密顿量(H(t)=H(0)(t)+\lambda V)的相互作用系统的密度算符收敛并产生熵。在状态空间中使用投影算符，密度算符被展开到微扰的所有阶次，然后进行重求和。与范霍夫[《物理学》21, 517 (1955)]及其他学者[U. 法诺，《现代物理评论》29, 74 (1959); U. 法诺，载于《多体问题讲座》第2卷，E. R. 卡涅洛编辑(学术出版社，纽约，1964); R. 兹万齐格，载于《理论物理讲座》第III卷，W. E. 布里顿、B. W. 唐斯和J. 唐斯编辑(威利跨学科出版社，纽约，1961)，第116 - 141页; K. M. 范弗利特，《数学物理杂志》19, 1345 (1978); K. M. 范弗利特，《加拿大物理学杂志》56, 1206 (1978)]早期的处理方法不同，我们得到了封闭表达式。由此我们建立了时间反演对称性质(P(γ,t|γ',t') = P(γ',t'|γ,t))，其中波浪号表示时间反演过程; 还推导了一个非平稳马尔可夫主方程。然后将时间反演对称应用于恒温系统，得到克鲁克斯 - 田崎涨落定理(FT)和量子雅津斯基功 - 能定理，以及一般熵涨落定理。详细讨论了功和熵的量子力学概念。最后，我们给出了马佐线性响应理论引理的非平衡扩展，通过这条替代途径得到了一些应用。
