2017/06/29 by Giovani L. Vasconcelos, Domingos S. P. Salazar, A. M. S. Macêdo · 8 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Complex Systems and Time Series Analysis #Entropy (arrow of time) #Mathematics #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1103/physreve.97.022104
published in Physical review. E 97(2), 022104 (American Physical Society) · 20 pages, 2 figures
arxiv created 2017/06/29 · openalex created_date 2017/07/14 · openalex publication_date 2018/02/05 · arxiv updated 2019/05/06 · openalex updated_date 2026/08/05
A formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem-representing the region where the measurements are made-in contact with a set of "nested heat reservoirs" corresponding to the hierarchical structure of the system, where the temperatures of the reservoirs are allowed to fluctuate owing to the complex interactions between degrees of freedom at different scales. The probability distribution function (pdf) of the temperature of the reservoir at a given scale, conditioned on the temperature of the reservoir at the next largest scale in the hierarchy, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H functions. The distribution of states of the small subsystem is then computed by averaging the quasiequilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017)10.1103/PhysRevE.95.032315] from a stochastic dynamical approach to the problem.