The non–zero value of Planck constant h underlies the emergence of several inequalities that must be satisfied in the quantum realm, the most prominent one being Heisenberg Uncertainty Principle. Among these inequalities, Bekenstein bound provides a universal limit on the entropy that can be contained in a localized quantum system of given size and total energy. In this Letter, we explore how Bekenstein bound is affected when Heisenberg uncertainty relation is deformed so as to accommodate gravitational effects close to Planck scale (Generalized Uncertainty Principle). By resorting to general thermodynamic arguments, and in regimes where the equipartition theorem still holds, we derive in this way a “generalized Bekenstein bound”. Physical implications of this result are discussed for both cases of positive and negative values of the deformation parameter.

普朗克常数h的非零值量子领域必须满足的几个不等式的出现，最突出的一个是海森堡测不准原理。在这些不等式中，Bekenstein 界对可以包含在给定大小和总能量的局域量子系统中的熵提供了一个普遍的限制。在这封信中，我们探讨了当海森堡不确定性关系变形以适应接近普朗克尺度（广义不确定性原理）的引力效应时，贝肯斯坦界如何受到影响。通过求助于一般热力学论证，并且在均分定理仍然成立的情况下，我们以这种方式推导出“广义贝肯斯坦界限”。针对变形参数的正值和负值这两种情况讨论了该结果的物理含义。