Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-10-11
Physics
Condensed Matter
Statistical Mechanics
6 pages, 4 figures, shortened for publication, some typos corrected
Scientific paper
The inverse relationship between energy and time is as familiar as Planck's constant. From the point of view of a system with many states, perhaps a better representation of the system is a vector of characteristic times (one per state) for example, a canonically distributed system. In the vector case the inverse relationship persists, this time as a relation between the $L_2$ norms. That relationship is derived herein. An unexpected benefit of the vectorized time viewpoint is the determination of surfaces of constant temperature in terms of the time coordinates. The results apply to all empirically accessible systems, that is situations where details of the dynamics are recorded at the microscopic level of detail. This includes all manner of simulation data of statistical mechanical systems as well as experimental data from actual systems (e.g. the internet, financial market data) where statistical physical methods have been applied.
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