Thermodynamic Behavior of Single Particle System in OneDimensional Φ4 Mean Field

Helmholtz’s theorem was used to study the thermodynamic behavior of a single particle system in a one-dimensional Φ~4 mean field. It analyzed the motion characteristics of particles and the dependence between the energy of the system and physical quantities such as temperature and entropy, and analyzed the changes that occur in the system. Thermodynamic behavior of the system was discussed. The results show that: as a simple dynamic system, the one-dimensional Φ~4 single-particle system also has the thermodynamic quantities of the macroscopic system, and on the basis of satisfying the thermodynamic relations, it shows the unique phase transition, negative heat capacity, and negative compression ratio such an abnormal thermodynamic behavior of the small system. These unique phenomena originate from the sudden change in the phase orbital space caused by a small increase in the system energy at the critical energy.The mechanism of negative heat capacity in this model can be used to explain the negative heat capacity phenomenon in atomic clusters such as Na, Ar, and Cu etc.