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Significant evidence is available to support the quantum effects of gravitythat leads to the generalized uncertainty principle (GUP) and the minimumobservable length. Usually quantum mechanics, statistical physics doesn't takegravity into account. Thermodynamic properties of ideal Bose gases in differentexternal power-law potentials are studied under GUP with statistical physicalmethod. Critical temperature, internal energy, heat capacity, entropy,particles number of ground state and excited state are calculated analyticallyto ideal Bose gases in the external potentials under GUP. Below the criticaltemperature, taking rubidium and sodium atoms ideal Bose gases whose particledensities are under standard and experimental conditions, respectively, asexamples, the relations of internal energy, heat capacity and entropy withtemperature are analyzed numerically. Theoretical and numerical calculationsshow that: GUP leads to an increase in the critical temperature. When thetemperature is lower than the critical temperature and slightly higher thanzero Kelvin, GUP's amendments to internal energy, heat capacity and entropy arepositive; As the temperature increases to a certain value, these amendmentsbecome negative. The external potentials can increase or decrease the influenceof GUP on thermodynamic properties. Under the initial experimental conditionswhen Bose-Einstein condensation was first verified by sodium atomic gas, theinfluence of GUP can be completely ignored. Under certain conditions, GUP maybecome the dominant factor governing the thermodynamic properties of thesystem.

Thermodynamic properties of ideal Bose gas trapped in different external power-law potentials under generalized uncertainty principle*