The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability distribution weighted by an exponential factor whose exponent is uniquely determined by the condition. We apply this theorem to explain the canonical equilibrium ensemble of a system in contact with a heat reservoir. Since the theorem only requires analysis at the level of the function of the subsystem and reservoir, it is applicable even without the knowledge of the composition of the reservoir itself, which extends the applicability of the canonical ensemble. Furthermore, we generalize our theorem to a model with strong interaction that contributes an additional term to the exponent, which is beyond the typical case of approximately additive functions. This result is new in both physics and mathematics, as a theory for the Gibbs conditioning principle for strongly correlated systems. A corollary provides a precise formulation of what a temperature bath is in probabilistic terms.

以整体函数的值为条件的子系统的函数的概率分布，在其值的比值变为零的极限中具有极限律：它等于由指数因子加权的无条件边际概率分布其指数由条件唯一决定。我们应用该定理来解释与储热器接触的系统的标准平衡系综。由于该定理仅需要在子系统和容器的功能级别上进行分析，因此即使在不知道容器本身的组成的情况下，该定理也是适用的，这扩展了规范集合的适用性。此外，我们将定理推广为具有强相互作用的模型，该模型为指数增加了一个附加项，这超出了近似加法函数的典型情况。作为有关强相关系统的吉布斯条件原理的理论，该结果在物理学和数学上都是新的。推论提供了概率论中温度浴的精确表述。