Porporato A, Rigby J R, Daly E
Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina, USA.
Phys Rev Lett. 2007 Mar 2;98(9):094101. doi: 10.1103/PhysRevLett.98.094101. Epub 2007 Feb 28.
The relative entropy between the joint probability distribution of backward and forward sequences is used to quantify time asymmetry (or irreversibility) for stationary time series. The parallel with the thermodynamic theory of nonequilibrium steady states allows us to link the degree of asymmetry in the time signal with the distance from equilibrium and the lack of detailed balance among its states. We study the statistics of time asymmetry in terms of the fluctuation theorem, showing that this type of relationship derives from simple general symmetries valid for any stationary time series.
前后序列联合概率分布之间的相对熵用于量化平稳时间序列的时间不对称性（或不可逆性）。与非平衡稳态热力学理论的平行关系使我们能够将时间信号中的不对称程度与离平衡态的距离及其状态间缺乏细致平衡联系起来。我们根据涨落定理研究时间不对称性的统计，表明这种关系源自对任何平稳时间序列都有效的简单一般对称性。
