2004/11/11 by B. H. Lavenda, Lavenda, B. H.
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0411304
6 pages
arxiv created 2004/11/11 · openalex publication_date 2004/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thermodynamics of power means applies to an ideal quantum gas which may be nonextensive. Transition to an ideal classical gas occurs when the empirical temperature exponents of the internal energy and absolute temperature coalesce. Limiting processes are pure heat conduction and pure deformations. Largest and smallest mean final volumes occur for isothermal and adiabatic processes, respectively. The increment in the heat admits two integrating factors which yield conserved quantities for adiabatic processes. Energy-conserving equilibrations yield the largest final means possible, while the second law follows from the property that the power means are monotonically increasing functions of their order. In the ideal classical gas limit, the change in the average entropy is proportional to the difference between the Shannon and Rényi entropies for nonextensive, isothermal systems that are multifractal in nature.