This paper uses Shannon’s entropy index to the base 2 to quantify the risk relative to the age at death in terms of bits (i.e. the amount of information revealed by tossing a fair coin). We first provide a simple decomposition of Shannon’s lifetime entropy index that allows us to analyse the determinants of lifetime entropy (in particular its relation with Wiener’s entropy of the event “death at a particular age conditional on survival to that age”) and to study how the risk about the duration of life is resolved as the individual becomes older. Then, using data on 37 countries from the Human Mortality Database, we show that, over the last two centuries, (period) lifetime entropy at birth has exhibited, in all countries, an inverted-U shape pattern with a maximum in the first half of the twentieth century (at 6 bits), and reaches, in the early twenty-first century, 5.6 bits for men and 5.5 bits for women. It is also shown that the entropy age profile shifted from a non-monotonic profile (in the eighteenth and nineteenth centuries) to a strictly decreasing profile (in the twentieth and twenty-first centuries).

中文翻译：

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从历史的角度看人类的一生熵（1750–2014）

本文使用香农熵指数（以2为底）来量化相对于死亡年龄的风险（以比特为单位）（即，抛掷公平硬币所揭示的信息量）。我们首先提供Shannon生命周期熵指数的简单分解，使我们能够分析生命周期熵的决定因素（尤其是它与事件“在特定年龄下的死亡取决于该年龄的死亡”事件的Wiener熵的关系），并研究如何随着年龄的增长，生命周期的风险得到了解决。然后，使用人类死亡率数据库中37个国家/地区的数据，我们发现，在过去的两个世纪中，所有国家/地区的出生时（生命周期）熵在整个过程中都呈现出倒U形，上半年最大并达到20世纪（6位）在二十一世纪初，男性为5.6位，女性为5.5位。还表明，熵年龄分布从非单调分布（在18和19世纪）转变为严格减小的分布（在20世纪和21世纪）。