Mathematical theory of thermodynamics of computation
Mathematical theory of thermodynamics of computation
复制标题
计算热力学数学理论
DOI：
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发表时间：
1992
影响因子：
2.5
通讯作者：
P. Vitányi
中科院分区：
文献类型：
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作者：
Ming Li;P. Vitányi
我们调查了一个新的研究领域：我们对从 x 到 y 计算的最终热力学成本感兴趣。除了其根本重要性之外，此类研究对于 VLSI 芯片的小型化和模式识别的应用具有潜在的影响。事实证明，热力学计算成本理论可以得到公理化的发展。我们的基本定理将物理学与数学联系起来，提供了使这种理论成为可能的关键。它建立了计算的最终热力学成本的最佳上限和下限。通过计算时间越来越长，耗散的能量越来越接近这些极限。事实上，人们可以用时间换取能量：存在一种可证明的时间-能量交易层次结构。基本定理还导出了热力学距离度量。该度量的拓扑特性表明邻域是稀疏的，如果它们以随机元素为中心，则邻域会变得更加稀疏。该证明以基本方式使用信息对称性。这些概念也在模式识别中得到应用。人们一直在寻找认知距离的客观概念来解释图片“相似性”的直观概念，但没有成功。热力学考虑导致了认知距离的递归不变概念。事实证明，热力学距离是一种通用的认知距离，它发现了任何认知距离所使用的所有有效特征。
We investigate a new research area: we are interested in the ultimate ther-modynamic cost of computing from x to y. Other than its fundamental importance , such research has potential implications in miniaturization of VLSI chips and applications in pattern recognition. It turns out that the theory of thermodynamic cost of computation can be axiomatically developed. Our fundamental theorem connects physics to mathematics , providing the key that makes such a theory possible. It establishes optimal upper and lower bounds on the ultimate thermodynamic cost of computation. By computing longer and longer, the amount of dissipated energy gets closer to these limits. In fact, one can trade time for energy: there is a provable time-energy trade-oo hierarchy. The fundamental theorem also induces a thermo-dynamic distance metric. The topological properties of this metric show that neighborhoods are sparse, and get even sparser if they are centered on random elements. The proofs use Symmetry of Information in a basic way. These notions also nd an application in pattern recognition. People have been looking without success for an objective notion of cognitive distance to account for the intuitive notion of`similarity' of pictures. Thermodynamic considerations lead to a recursively invariant notion of cognitive distances. It turns out that the thermodynamic distance is a universal cognitive distance which discovers all eeective features used by any cognitive distance whatsoever.