发表机构
Institute for Functional Intelligent Materials, National University of Singapore; Department of Mathematics, National University of Singapore（新加坡国立大学功能智能材料研究所; 新加坡国立大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究可分希尔伯特空间上平稳扩散的熵产生，通过可逆-不可逆漂移分解和不变测度建立下界，并给出有限与无限熵产生的条件及非线性无穷秩示例。
AI 中文摘要
我们研究可分希尔伯特空间上平稳扩散的熵产生，其中协方差算子可能是退化的且状态依赖的，并具有迹类性质。我们首先定义可逆-不可逆漂移分解，为反向动力学提供候选漂移。然后直接利用不变测度，我们建立了以不可逆漂移的扩展平稳Cameron-Martin能量表示的下界，无需平稳反向过程的扩散表示。该下界表明当能量为无穷时熵产生为无穷，并且我们在有限能量情形下建立了等式成立的充分条件。我们还发展了互补准则，分别将平稳反向过程识别为具有常数或连续状态依赖扩散系数的希尔伯特空间扩散。提供了两个非线性无穷秩例子，表明有限熵产生并不要求不可逆漂移位于协方差的值域内，而即使系数全局Lipschitz且协方差可逆，熵产生也可能为无穷。
英文摘要
We study entropy production for stationary diffusions on separable Hilbert spaces with possibly degenerate, state-dependent trace-class covariance. We first define the reversible--irreversible drift decomposition to provide a candidate drift for the reversed dynamics. Then by working directly with the invariant measure, we establish a lower bound in terms of the extended stationary Cameron--Martin energy of the irreversible drift, without requiring a diffusion representation of the stationary reversal. The bound implies infinite entropy production when the energy is infinite and we establish sufficient conditions for equality in the finite-energy regime. We also develop complementary criteria for identifying the stationary reversal as a Hilbert-space diffusion with constant or continuous state-dependent diffusion coefficients, respectively. Two nonlinear infinite-rank examples are provided to show that finite entropy production does not require the irreversible drift to lie in the covariance range, whereas entropy production may be infinite even with globally Lipschitz coefficients and injective covariance.
Comments26 pages
