Theoretical Study of Variable Measurement Uncertainty $h_I$ and Infinite Unobservable Entropy

This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=\bigtriangleup x_i\bigtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured information of a system but the maximum entropy remains constant due to the uncertainty principle. By taking $h_u\rightarrow 0^+$ an infinite unobservable entropy is attained leading to an infinite unobservable energy per particle and an unobservable chemical equilibrium between all particles. The amount of heat fluxing though measurement apparatus is formulated as a function of $h_I$ for systems in steady state equilibrium as well as the number of measured particles or sub-particles so any system can be described as unitary or composite in number. Some example systems are given using variable $h_I$.