The idea that the temperature of the universe will never reach absolute zero, even after the Heat Death, is based on our current understanding of the laws of thermodynamics and the behavior of empty space. There are a few reasons why empty space is expected to have a minimum temperature, known as the residual or background temperature.
Cosmic Microwave Background (CMB) radiation: The universe is filled with cosmic microwave background radiation, which is a remnant of the Big Bang. This radiation permeates all of space and has a uniform temperature of about 2.7 Kelvin above absolute zero. This temperature is known as the CMB temperature or the residual temperature of the universe. Even in the absence of matter, this background radiation exists and contributes to the minimum temperature.
Zero-point energy: According to quantum mechanics, empty space is not truly empty but is filled with quantum fluctuations. These fluctuations give rise to what is known as zero-point energy. Zero-point energy refers to the lowest possible energy state that particles can have, even at absolute zero temperature. This means that even in the absence of external energy, empty space possesses inherent energy. As a consequence, it prevents the temperature from reaching absolute zero.
Entropy: The concept of entropy is intimately connected with temperature. Entropy is a measure of the disorder or number of microstates available to a system. In a system with a non-zero temperature, there is always some level of entropy present. As the universe expands and evolves towards the Heat Death, the entropy is expected to increase significantly. At the Heat Death, the universe will reach its maximum entropy state, but this state will still have a residual temperature associated with it, as explained by the other factors mentioned above.
It's important to note that our understanding of the ultimate fate of the universe and the behavior of empty space at extremely long timescales is still an active area of research. The concepts related to the Heat Death and the minimum temperature of the universe are based on current theories and observations, but future discoveries could potentially refine or expand our understanding of these ideas.