In recent years, great efforts are devoted to reducing the work cost of the bit operation, but it is still unclear whether these efforts are sufficient for resolving the temperature stabilization problem in computation. By combining information thermodynamics and a generalized constitutive model which can describe Fourier heat conduction as well as non-Fourier heat transport with nonlocal effects, we here unveil two types of the thermodynamic costs in the temperature stabilization problem. Each type imposes an upper bound on the amount of bits operated per unit time per unit volume, which will eventually limit the speed of the bit operation. The first type arises from the first and second laws of thermodynamics, which is independent of the boundary condition and can be circumvented in Fourier heat conduction. The other type is traceable to the third law of thermodynamics, which will vary with the boundary condition and is ineluctable in Fourier heat conduction. These thermodynamic costs show that reducing the work cost of the bit operation is insufficient for resolving the temperature stabilization problem in computation unless the work cost vanishes.

中文翻译：

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逻辑不可逆计算中温度稳定的热力学成本

近年来，人们致力于降低位运算的工作成本，但仍不清楚这些努力是否足以解决计算中的温度稳定问题。通过结合信息热力学和广义本构模型（可以描述傅里叶热传导以及具有非局部效应的非傅里叶热传输），我们在这里揭示了温度稳定问题中的两种类型的热力学成本。每种类型都对单位体积、单位时间操作的位数施加上限，这最终会限制位操作的速度。第一类源于热力学第一定律和第二定律，与边界条件无关，可以在傅里叶热传导中规避。另一种类型可以追溯到热力学第三定律，它会随着边界条件的变化而变化，并且在傅立叶热传导中是不可避免的。这些热力学成本表明，除非工作成本消失，否则降低位操作的工作成本不足以解决计算中的温度稳定性问题。