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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Information and contact geometric description of expectation variables exactly derived from master equations
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Information and contact geometric description of expectation variables exactly derived from master equations

机译：信息和联系几何描述预期从主方程派生的变量

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摘要

In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of a set of appropriately chosen Markov kernels. To geometrize such dynamical systems for expectation variables, information geometry is used for expressing equilibrium states, and contact geometry is used for nonequilibrium states. Here time-developments of the expectation variables are identified with contact Hamiltonian vector fields on a contact manifold. Also, it is shown that the convergence rate of this dynamical system is exponential. Duality emphasized in information geometry is also addressed throughout.
机译：In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of a set of appropriately chosen Markov kernels. 为了使这种用于期望变量的这种动态系统，信息几何形状用于表示平衡状态，并且接触几何形状用于非QuiLibiRigium状态。 在这里，预期变量的时间发展是用联系人歧管上的联系Hamiltonian矢量字段识别的。 而且，表明该动态系统的收敛速率是指数的。 在整个信息几何中强调的二元性也是解决的。

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