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→Radiative arrow of time
Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves, so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,<!-- ref></ref --> making the latter contradictory to the second law of thermodynamics in usual circumstances.
Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations accommodate solutions of convergent waves as well as radiative ones. This arrow has been reversed in carefully worked experiments that created convergent waves, so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it,<!-- ref></ref --> making the latter contradictory to the second law of thermodynamics in usual circumstances.
虽然波动方程包含了会聚波和辐射波的解，但所有的波，从无线电波到声波，再到石头扔进池塘里产生的波，都是从源头向外扩展。这个方向在精心设计的产生收敛波的实验中被颠倒过来，所以这个方向可能来自热力学方向，因为满足产生收敛波的条件比产生辐射波的条件需要更多的次序。换句话说，产生会聚波初始条件的概率远低于产生辐射波初始条件的概率。事实上，正常情况下，辐射波会增加熵，而会聚波会减少熵，<!-- ref></ref -->而后者在通常情况下与热力学第二定律相矛盾。
虽然波动方程包含了会聚波和辐射波的解，但所有的波，从无线电波到声波，再到石头扔进池塘里产生的波，都是从源头向外扩展。这个方向在精心设计的产生收敛波的实验中被颠倒过来，所以这个方向可能来自热力学方向，因为满足产生收敛波的条件比产生辐射波的条件需要更多的次序。换句话说，产生会聚波初始条件的概率远低于产生辐射波初始条件的概率。事实上，正常情况下，辐射波会增加熵，而会聚波会减少熵，<!-- ref></ref -->而后者与通常情况下的热力学第二定律相矛盾。
=== Causal arrow of time ===
=== Causal arrow of time ===