熵变和不可见的低能态：防御性联盟的例子
Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example
摘要：
较低的温度导致访问低能态的概率更高。这种直觉信念是大多数物理学启发的解决困难优化问题的策略的基础。例如，如果适当地降低温度，则流行的模拟退火（SA）动力学被期望接近基态。在这里，我们证明，这种信念并不总是合理的。具体来说，我们采用腔的方法来分析最小的强防御联盟问题，并发现在解空间中的分歧，诱导的熵-能量分布的拐点。虽然容易获得的配置与较低的自由能分支相关联，但在相同的温度范围内，低能量配置与较高的自由能分支相关联。在高能组态和基态之间存在不连续的相变，这通常不能被SA跟随。我们引入了一个能量钳位策略，以获得更高的自由能分支，克服SA的局限性的优越的解决方案。
英文摘要：
Lower temperature leads to a higher probability of visiting low-energy states. This intuitive belief underlies most physics-inspired strategies for addressing hard optimization problems. For instance, the popular simulated annealing (SA) dynamics is expected to approach a ground state if the temperature is lowered appropriately. Here we demonstrate that this belief is not always justified. Specifically, we employ the cavity method to analyze the minimum strong defensive alliance problem and discover a bifurcation in the solution space, induced by an inflection point in the entropy--energy profile. While easily accessible configurations are associated with the lower-free-energy branch, the low-energy configurations are associated with the higher-free-energy branch within the same temperature range. There is a discontinuous phase transition between the high-energy configurations and the ground states, which generally cannot be followed by SA. We introduce an energy-clamping strategy to obtain superior solutions by following the higher-free-energy branch, overcoming the limitations of SA.
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