Schottky anomaly of Reissner-Nordström-de Sitter spacetime  

作　　者：Hai-Long Zhen Yu-Bo Ma Huai-Fan Li Li-Chun Zhang Yun-Zhi Du 甄海龙;马宇波;李怀繁;张丽春;杜云芝(Department of Physics,Shanxi Datong University,Datong 037009,China;Institute of Theoretical Physics,Shanxi Datong University,Datong,037009,China;Shanxi College of Technology,College of General Education,Shuozhou 036000,China)

机构地区：[1]Department of Physics,Shanxi Datong University,Datong 037009,China [2]Institute of Theoretical Physics,Shanxi Datong University,Datong,037009,China [3]Shanxi College of Technology,College of General Education,Shuozhou 036000,China

出　　处：《Chinese Physics C》2025年第3期203-212,共10页中国物理C(英文版)

基　　金：Supported by the Natural Science Foundation of China(12375050,11705106,12075143);the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province,China(2023L269);the Science Foundation of Shanxi Datong University(2022Q1,2020Q2);the Natural Science Foundation of Shanxi Province,China(202203021221209,202303021211180);the Teaching Reform Project of Shanxi Datong University(XJG2022234)。

摘　　要：In the extended thermodynamics of black holes,there exists a thermodynamical pressure whose dual thermodynamical quantity is volume.Extensive studies have been conducted on the phase structure of numerous black holes,demonstrating striking similarities to the phase structures of various ordinary matter systems.From a comparison between the thermodynamic properties of spherically symmetric AdS black holes and ordinary thermodynamic systems,we know that the isovolumetric heat capacity of the former is zero,whereas that of the latter is non-zero.The intrinsic reason for this discrepancy is a topic of interest.For Reissner-Nördstrom-de Sitter(RN-dS)spacetime with the coexistence of the black hole and cosmological horizons,the effective thermodynamic quantities are presented alongside the interaction between two horizons.The heat capacity in RN-dS spacetime is then investigated,and it is demonstrated that the behavior of the heat capacity in RN-dS spacetime is analogous to that of Schottky specific heat.Treating two horizons in RN-dS spacetime as two distinct energy levels in a two-energy-level system,we investigate the thermodynamic properties in RN-dS spacetime by studying the thermodynamic properties in an ordinary two-energy system,thereby elucidating the intrinsic reasons for the occurrence of Schottky specific heat in RN-dS spacetime.The heat capacity observed in RN-dS spacetime is not only consistent with that of Schottky specific heat described by the effective thermodynamic quantities in RN-dS spacetime but also with that of an ordinary two-energy-level system.These results not only reveal the quantum properties of RN-dS spacetime but also provide a new avenue for further in-depth study of the quantum properties of black holes and dS spacetime.

关 键 词：de Sitter spacetime effective thermodynamic quantities heat capacity Schottky specific heat 

分 类 号：P14[天文地球—天体物理]