This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=?igtriangleup x_i?igtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured entropy of a system but the maximum entropy remains constant due to the uncertainty principle. By taking $h_u ightarrow 0^+$ 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 $h_I$.
Worcester Polytechnic Institute
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Vanslette, Kevin M., "Theoretical Study of Variable Measurement Uncertainty h_I and Infinite Unobservable Entropy" (2013). Masters Theses (All Theses, All Years). 289.
Entropy, Infinite, Heat, Information, Uncertainty, Measurement