Abstract This paper makes a novel linkage between the multiple-computations theorem in philosophy of mind and Landauer's principle in physics. The multiple-computations theorem implies that certain physical systems implement simultaneously more than one computation. Landauer's principle implies that the physical implementation of “logically irreversible” functions is accompanied by minimal entropy increase. We show that the multiple-computations theorem is incompatible with, or at least challenges, the universal validity of Landauer's principle. To this end we provide accounts of both ideas in terms of low-level fundamental concepts in statistical mechanics, thus providing a deeper understanding of these ideas than their standard formulations given in the high-level terms of thermodynamics and cognitive science. Since Landauer's principle is pivotal in the attempts to derive the universal validity of the second law of thermodynamics in statistical mechanics, our result entails that the multiple-computations theorem has crucial implications with respect to the second law. Finally, our analysis contributes to the understanding of notions, such as “logical irreversibility,” “entropy increase,” “implementing a computation,” in terms of fundamental physics, and to resolving open questions in the literature of both fields, such as: what could it possibly mean that a certain physical process implements a certain computation.

中文翻译：

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实现逻辑的物理学：兰道尔原理和多重计算定理

摘要本文将心算的多重计算定理与兰道尔的物理学原理联系起来。多重计算定理意味着某些物理系统同时执行多个计算。Landauer的原理意味着“逻辑上不可逆”函数的物理实现伴随着最小的熵增加。我们证明了多重计算定理与兰道尔原理的普遍有效性是不相容的，或者至少是挑战。为此，我们从统计力学的低级基本概念入手，对这两种思想进行了说明，因此，与从热力学和认知科学的高级术语中给出的标准表达相比，它们对这些思想有更深入的了解。自Landauer' s的原理对于试图推导热力学第二定律在统计力学中的普遍有效性至关重要，我们的结果表明，多重计算定理对第二定律具有至关重要的意义。最后，我们的分析有助于理解基本逻辑方面的概念，例如“逻辑不可逆性”，“熵增加”，“实现计算”，以及解决这两个领域的文献中的未解决问题，例如：这可能意味着某个物理过程实现了某个计算。