Dependence of dissipation on the initial distribution over states
Dependence of dissipation on the initial distribution over states
复制标题
DOI：
10.1088/1742-5468/aa7ee1
复制
发表时间：
2017-08-01
影响因子：
2.4
通讯作者：
Wolpert, David H.
中科院分区：
文献类型：
--
作者：
Kolchinsky, Artemy;Wolpert, David H.
我们分析了一个固定的非平衡过程所耗散的功是如何依赖于初始状态分布的。具体地说，我们比较了当过程与某些指定的初始分布使用时的耗散量与任何初始分布可能的最小耗散量。我们证明了这两个耗散量之间的差异是由一个简单的信息理论函数给出的，该函数仅取决于初始和最终状态分布。至关重要的是，这种差异与与这些分布相关的过程细节无关。然后，我们考虑耗散如何依赖于“计算机”的初始分布，即一个非平衡过程，其粗粒度宏观状态的动力学实现了一些期望的输入输出映射。我们表明，当以计算机粗粒度宏观状态的分布来陈述时，我们的结果仍然适用。这可以看作是一种新的热力学计算成本，反映了输入分布的变化，而不是计算的逻辑动态。
We analyze how the amount of work dissipated by a fixed nonequilibrium process depends on the initial distribution over states. Specifically, we compare the amount of dissipation when the process is used with some specified initial distribution to the minimal amount of dissipation possible for any initial distribution. We show that the difference between those two amounts of dissipation is given by a simple information-theoretic function that depends only on the initial and final state distributions. Crucially, this difference is independent of the details of the process relating those distributions. We then consider how dissipation depends on the initial distribution for a 'computer', i.e. a nonequilibrium process whose dynamics over coarse-grained macrostates implement some desired input-output map. We show that our results still apply when stated in terms of distributions over the computer's coarse-grained macrostates. This can be viewed as a novel thermodynamic cost of computation, reflecting changes in the distribution over inputs rather than the logical dynamics of the computation.