Abstract
We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.
Highlights
The growth of structures from the initial condition in the early Universe to the galaxies and clusters of galaxies is addressed by the standard model of cosmology
There is another approach to structure formation theory from the statistical mechanics point of view, where the structures form when a phase transition occurs in gravitating systems [7,8,9,10,11,12,13,14,15,16,17,18,19,20]
We have studied thermodynamical phase transition under MONDian gravity
Summary
The growth of structures from the initial condition in the early Universe to the galaxies and clusters of galaxies is addressed by the standard model of cosmology. The standard paradigm for structure formation, Λ Cold Dark Matter (ΛCDM) [1], has a very good agreement in the early Universe from the CMB observations [2] because the free parameters are tuned to fit the CMB; ΛCDM runs into severe difficulties with local and largescale structures [3,4,5,6] There is another approach to structure formation theory from the statistical mechanics point of view, where the structures form when a phase transition occurs in gravitating systems [7,8,9,10,11,12,13,14,15,16,17,18,19,20].
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