Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking (black hole) entropy, which relates the entropy to the crosssectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes: Schwarzschild, Garfinkle-Horowitz-Strominger and Reissner-Nordström is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be positive. The entropy S, which is assumed to be related to horizon's two-dimensional area, gets an additional terms, for instance 2 √ πα √ S, where α is the GUP parameter.

PACS 25.75.-q -Relativistic heavy-ion nuclear reactions PACS 25.75.Dw -Particle production (relativistic collisions) PACS 24.85.+p -Quantum chromodynamics in nuclei Abstract -The strange-quark occupation factor (γs) is determined from the statistical fit of the multiplicity ratio K + /π + in a wide range of nucleon-nucleon center-of-mass energies ( √ sNN ).From this single-strange-quark-subsystem, γs( √ sNN ) was parametrized as a damped trigonometric functionality and successfully implemented to the hadron resonance gas model, at chemical semi-equilibrium. Various particle ratios including K − /π − , Λ/π − , andΛ/π − are well reproduced. The phenomenology of γs( √ sNN ) suggests that, the hadrons (γs raises) at √ sNN ≃ 7 GeV seems to undergo a phase transition to a mixed phase (γs declines), which is then derived into partons (γs remains unchanged with increasing √ sNN ), at √ sNN ≃ 20 GeV.

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Inspired by Lifshitz theory for quantum critical phenomena in condensed matter, Horava proposed a theory for quantum gravity with an anisotropic scaling in ultraviolet. In Horava-Lifshitz gravity (HLG), we have studied the impacts of six types of equations of state on the evolution of various cosmological parameters such as Hubble parameters and scale factor. From the comparison of the general relativity gravity with the HLG with detailed and without with non-detailed balance conditions, remarkable differences are found. Also, a noticeable dependence of singular and non-singular Big Bang on the equations of state is observed. We conclude that HLG explains various epochs in the early universe and might be able to reproduce the entire cosmic history with and without singular Big Bang. approach benefits from the success of QFT in describing all forces (except gravity so-far) and the standard model of the elementary particles. The scalar field theory, that was proposed by Lifshitz in order to explain the quantum critical phenomena in condensed matter [4], inspired Horava to propose a theory for the quantum gravity with an anisotropic scaling in UV. This new approach is thus known as Horava-Lifshitz gravity (HLG) [5,7,8,9,10,11,12,13,14,15], where the dynamical critical exponent (z) makes the theory non-relativistic.In analogy to critical systems, the UV fixed point has been treated [16]. The HLG approach assures causal dynamical triangulations [17], renormalization group approaches based on asymptotic safety [18,19] and symmetries of GR. This approach was discussed in an extensive amount of literature [20,21,22], where problems such as, internal consistency and compatibility with observations are treated, as well. The new dimensionless coupling λ is assumed to approach unity in the infrared (IR) limit with the argumentation that at the HLG-charactering parameter λ = 1, HLG theory can't be reduced to GR. For the sake of completeness, we mention that this is not always the case for all HLG models [23].Recent astrophysical observations obviously indicate that the universe expands with an accelerating rate, probably due to dark energy [24,25]. Besides inflation, a series of symmetry-breaking phase transitions, where topological defects may have been formed [26], were conjecture to take place. On the other hand, the HLG-type approach [5] proposes that the modification in gravity is responsible for the accelerated expansion of the universe.Furthermore, various modified theories for gravity can be implemented [27,28]. They successfully unify various inflation models with the late-time acceleration and cosmological observations. But when endorsing any proposal about (non)singular Big Bang due to controversial quantum gravity approaches such as generalized uncertainty principle (GUP) and modified dispersion relation (MDR) [29] should be seen as unwarranted claims. the Big Bang singularity is a fundamental problem, which should be tackled by a good quantum gravity theory, such as HLG or even better.The present paper is organiz...