Black holes violate the third law of thermodynamics in its standard formulation. Schwarzschild black hole entropy is inverse proportional to the square of the temperature \(S=1/(16 \pi T^2)\) and tends to infinity rather than zero when the temperature goes to zero. We search for quantum statistical models with such exotic thermodynamic behaviour. It is shown that the Schwarzschild black hole in \(D=4\) spacetime dimensions corresponds to a Bose gas in a space with \(d=-4\) negative spatial dimensions. The Riemann zeta function is used to define the entropy of the Bose gas in negative dimension. The correspondence between black holes in higher dimensions and de Sitter space with Bose gas is considered. In particular case of \(D=5\), the corresponding Bose gas model lives in a space with \(d=3\) spatial dimensions and contains a nonlocal kinetic term.

黑洞的标准表述违反了热力学第三定律。史瓦西黑洞熵与温度的平方\(S=1/(16\pi T^2)\)成反比，并且当温度趋于零时趋于无穷大而不是零。我们寻找具有这种奇异热力学行为的量子统计模型。结果表明，\(D=4\)时空维度的史瓦西黑洞对应于\(d=-4\) 负空间维度的玻色气体。黎曼 zeta 函数用于定义负维度玻色气体的熵。考虑了高维黑洞和德西特空间与玻色气体之间的对应关系。在\(D=5\)的特定情况下，相应的玻色气体模型存在于具有\(d=3\)空间维度的空间中，并且包含非局域动力学项。