2014/10/20 by T. M. Shih, Z. J. Gao, Zong-Mao Gao +12
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Physics (physics.comp-ph) #FOS: Physical sciences #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.1410.5195
11 pages, 12 figures
openalex publication_date 2014/10/20 · arxiv created 2014/10/21 · arxiv updated 2014/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an isolated assembly that comprises a system and its surrounding reservoirs, the total entropy (Sa) always monotonically increases as time elapses. This phenomenon is known as the second law of thermodynamics (Sa≥0). Here we analytically prove that, unlike the entropy itself, the entropy variation rate (B=dSa/dt) defies the monotonicity for multiple reservoirs (n≥2). In other words, there always exist minima. For example, when a system is heated by two reservoirs from T=300 K initially to T=400 K at the final steady state, B decreases steadily first. Then suddenly it turns around and starts to increases at 387 K until it reaches its steady-state value, exhibiting peculiar dipping behaviors. In addition, the crux of our work is the proof that a newly-defined variable, B/T, always decreases. Our proof involves the Newton's law of cooling, in which the heat transfer coefficient is assumed to be constant. These theoretical macro-scale findings are validated by numerical experiments using the Crank-Nicholson method, and are illustrated with practical examples. They constitute an alternative to the traditional second-law statement, and may provide useful references for the future micro-scale entropy-related research.