Related papers: Fractal geometry, information growth and nonextens…
We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness, at any scale, of the…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…
The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and thermofractals. After reviewing this connection, we…
The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $\omega$ which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the…
It is shown that there is a mapping of the replica approach to disordered systems with finite replica index $n$ on the Tsallis non-extensive statistics, if the average thermodynamic entropy differs from the information entropy for the…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition…
This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to explain the fractal dimension of urban form. The…
The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical…
In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand…
We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the…
The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years,…
The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…
Simple time-reversible systems can generate {\it irreversible} flows satisfying the Second Law of Thermodynamics. Maps, and equivalent random walks, can also do this. We study a pair of time-reversible Baker Maps, $N2$ and $N3$, which…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
The nonextensive statistics based on the $q$-entropy $S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems in which the $q$ value is uniformly distributed. For the systems containing different $q$'s, the…