The assumption that entropy calculations ignore correlations among variables in a system is not universally true but is often made for simplicity and practicality in certain contexts. This assumption is particularly relevant in classical statistical mechanics and thermodynamics.
In classical thermodynamics, entropy is defined as a measure of the system's disorder or the number of microstates that correspond to a given macrostate. It is calculated based on the probabilities of different microstates and the assumption of equal a priori probabilities when the system's information is incomplete. This approach assumes that the system is in a state of maximum entropy, which corresponds to maximum ignorance about the system's exact microstate.
By ignoring correlations among variables, calculations of entropy become significantly simpler. It allows treating each variable independently, which simplifies the mathematical calculations and reduces the computational complexity. This assumption is often valid for macroscopic systems where the number of particles is extremely large, and interactions between particles can be approximated as statistical averages.
However, in situations where correlations between variables are significant or when dealing with microscopic or quantum systems, the assumption of ignoring correlations becomes inadequate. In these cases, more sophisticated techniques, such as quantum statistical mechanics or information theory, are used to account for correlations and obtain more accurate entropy calculations.
It's important to note that in quantum systems, entanglement is a form of correlation that plays a crucial role and cannot be ignored. The study of entropy in quantum systems involves considering the entanglement between subsystems and using measures like entanglement entropy or von Neumann entropy to quantify the system's information content.
In summary, while the assumption of ignoring correlations among variables is often made for simplicity in classical statistical mechanics and thermodynamics, it may not hold in all cases, especially when dealing with quantum systems or situations where correlations play a significant role.