2005/10/11 by David Ford, Ford, David · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Data Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an) #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #physics.data-an
paper · pdf · doi:10.48550/arxiv.cond-mat/0510291
6 pages, 4 figures, shortened for publication, some typos corrected
openalex publication_date 2005/10/11 · arxiv created 2006/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L2 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.