New Horizons in Mathematical Physics

Download PDF (1103.1 KB) PP. 53 - 73 Pub. Date: June 1, 2019

DOI: 10.22606/nhmp.2019.32002

• Zhong-Cheng Liang^*
  School of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing, China

A theory of cluster ensemble statistics is developed based on the body particle model. Cluster ensemble is a set of temporal snapshots of particle configuration, which is accurately described by a cluster matrix. The partition functions of liquid, solid and gas are calculated in the statistical zones of the energy space, which directly reveals the relationship between the volume and motional energies. The motional energies of liquid, solid and gas are expressed by the statistical correlations of the particle mass, the rotary inertia and the elastic modulus, respectively. Complete energy relations and equations are derived through the statistics of cluster ensemble. Thermodynamic laws and equations can be logically inferred from the theoretical results. Two types of phase transition mechanism are analyzed based on the theory of body particles and the structure of the energy space.

Particle and cluster, ensemble statistics, partition function, order parameter, thermodynamic laws, phase transition

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