Fisher information is a cornerstone of both statistical inference and physical theory, leading to debate about whether its latter role is active or passive. Motivated by connections between Fisher information, entropy, and the quantum potential in the de Broglie–Bohm causal interpretation of quantum mechanics, the purpose of this article is to derive the position probability density when there a is a close and ubiquitous bonding of Fisher information and quantum potential. This is done by exploring a case in which a particle moves in a straight line and the integrands in Fisher information and expected quantum potential are proportional. It is found that in this case the probability density given by the Schrödinger wave equation has a Laplace distribution and that quantum potential is a negative constant at all points and times. It is noted that the rate of change of the entropy of the particle is bounded above by a limit that is proportional to the square roots of both Fisher information and the absolute value of quantum potential. Unlike Fisher information, quantum potential is a measure of a real physical potential, and it is proposed that it is quantum potential that puts an upper bound on the rate of change of the particle’s entropy and that, being negative in this case, may also act to contain the particle on its straight-line path. It is suggested that Fisher information does not have an active role in the physics, at least in this case, and only provides information about entropy.

Fisher信息是统计推论和物理理论的基石，引发了关于其后继作用是主动还是被动的争论。受费舍尔信息，熵和de Broglie-Bohm因果关系因果解释中的量子势之间的联系的激励，本文的目的是在存在费舍尔信息和无处不在的紧密结合时推导位置概率密度。量子势。这是通过研究粒子沿直线移动且Fisher信息中的被积物与预期量子势成正比的情况来完成的。发现在这种情况下，薛定ding波动方程给出的概率密度具有拉普拉斯分布，并且量子势在所有时间点都是负常数。应当指出，粒子的熵的变化率在上面被限制，该限制与费舍尔信息的平方根和量子势的绝对值成比例。与费舍尔信息不同，量子势是对实际物理势的量度，有人提出，是量子势将粒子熵的变化率置于上限，并且在这种情况下为负，也可能起作用将粒子包含在其直线路径上。建议费舍尔信息至少在这种情况下在物理学中不起作用，而仅提供有关熵的信息。