Violating the second law of thermodynamics in a dynamical system through equivalence closure via mutual information carriers of a 5-tuple measure space

Time and space average of an ergodic systems following the 5-tuple relations (A,~,J,Σ,μ) through the initial increment from a+bθ to a+c+bθ indicates the entropy to be reserved in the deterministic yet dynamical and conservative systems to hold for the set S_p= S_1 ∑_(i=2)^∞_S_i keeping S as the entropy ∃(S_∞=⋯S_3=S_2 )>S_1 obeying the Poincare ́ recurrence theorem throughout the constant attractor A. This in turn states the facts of the equivalence closure as the property of the induced systems to resemblance an entropy conserving scenarios.

Violating the second law of thermodynamics in a dynamical system through equivalence closure via mutual information carriers of a 5-tuple measure space

Time and space average of an ergodic systems following the 5-tuple relations (A,~,J,Σ,μ) through the initial increment from a+bθ to a+c+bθ indicates the entropy to be reserved in the deterministic yet dynamical and conservative systems to hold for the set S_p= S_1 ∑_(i=2)^∞_S_i keeping S as the entropy ∃(S_∞=⋯S_3=S_2 )>S_1 obeying the Poincare ́ recurrence theorem throughout the constant attractor A. This in turn states the facts of the equivalence closure as the property of the induced systems to resemblance an entropy conserving scenarios.

Statistical Mechanics: The Basics

This chapter introduces the reader to the basics of statistical mechanics. Gibbsian and neo-Boltzmannian approaches are outlined. It includes a statistical-mechanical analogue of the second law of thermodynamics, and a proof of the Poincaré recurrence theorem. It is argued that the differences between Gibbsian and neo-Boltzmannian approaches have been exaggerated.

SHRINKING TARGET PROBLEM FOR RANDOM IFS

We describe the shrinking target problem for random iterated function systems which are semi-conjugate to random subshifts. We get the Hausdorff dimension of the set based on shrinking target problems with given targets. The main idea is an extension of ubiquity theorem which plays an important role to get the lower bound of the dimension. Our method can be used to deal with the sets with respect to more general targets and the sets based on the quantitative Poincaré recurrence properties.