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Thermofractal

Thermofractals are thermodynamics systems with a fractal structure in the energy-momentum space. There are two types of thermofractals, each one with the following properties:

1) It is a thermodynamical system with total energy U=E+K, and a complex structure with a number N of compound systems that present the same properties as the parent system. Here, E is the total internal energy of the N components, and K their total kinetic energy.

2) In the case of the thermofractal type-I, the internal energy, E, and the kinetic energy, K, of each compound system are such that the ratio ε/λ=E/K follows a distribution P(ε). In the case of the thermofractal type-II, the ratio ε/λ=E/U follows a distribution P(ε). Here, λ is a scaling parameter.

3) At some level of the internal structure, the fluctuations of the internal energy of the compound systems are small enough to be disregarded, and then their internal energy can be regarded as constant. The choice of the level is associated with λ and breaks the scaling symmetry.

The thermofractals present [| q-exponential distributions], and are best described by the [| non-additive entropy] and the [| Tsallis Statistics] introduced by [| Constantino Tsallis]. The entropic index, q, in the Tsallis distribution can be calculated in terms of the parameters of the thermofractal structure, representing the number of [| degrees of freedom] of the thermofractal.

In the context of [| particle physics], thermofractals were associated with the [|Non-extensive Self-consistent Thermodynamics theory], a generalization of the [| Self-Consistent Principle] proposed by [| Rolf Hagedorn], resulting in the [|Non-Extensive Self-Consistent Thermodynamics]. The systems described by the [| Yang-Mills Theory] allows the formation of thermofractal structures. A review on the subject can be found in Fractal Structures of Yang–Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics.

The thermofractal of type-I was used in [| information theory] diffused in a [| scale-free network] and used to analyse data on [| COVID-19] spreading dynamics.