Statistical mechanics of exploding phase spaces: ontic open systems

Pazuki, Roozbeh H.; Pruessner, Gunnar; Tempesta, Piergiulio

doi:10.1088/1751-8121/aad57b

Cited by 31 publications

(59 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, see [11]. In this paper we show that it is indeed possible to find a complete classification of complex stochastic systems, including the super-exponential case.…”

Section: ( )mentioning

confidence: 66%

“…These coins are magnetic, so that any two can stick to each other to create a pair which is a third state obtained by interactions of elements (one possible configuration). As mentioned before, in [11] it is shown that the phasespace volume can be obtained recursively…”

Section: Super-exponential Growth: Magnetic Coinsmentioning

confidence: 88%

“…Stochastic systems with elements that can occupy several states (more than one) and that can form structures with other elements, are generally super-exponential systems. It was pointed out in [11] that such systems might exhibit non-trivial thermodynamical properties.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Classification of complex systems by their sample-space scaling exponents

2018

View full text Add to dashboard Cite

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W(N) depends on the size N of the system. Here we propose a scaling expansion of the phasespace volume W(N) of a stochastic system. The corresponding expansion coefficients (exponents) define the universality class the system belongs to. Systems within the same universality class share the same statistics and thermodynamics. For subexponentially growing systems such expansions have been shown to exist. By using the scaling expansion this classification can be extended to all stochastic systems, including correlated, constraint and super-exponential systems. The extensive entropy of these systems can be easily expressed in terms of these scaling exponents. Systems with super-exponential phasespace growth contain important systems, such as magnetic coins that combine combinatorial and structural statistics. We discuss other applications in the statistics of networks, aging, and cascading random walks.

show abstract

“…, see [11]. In this paper we show that it is indeed possible to find a complete classification of complex stochastic systems, including the super-exponential case.…”

Section: ( )mentioning

confidence: 66%

Section: Super-exponential Growth: Magnetic Coinsmentioning

confidence: 88%

See 1 more Smart Citation

Classification of complex systems by their sample-space scaling exponents

2018

View full text Add to dashboard Cite

show abstract

“…In addition, the results are applied for the derivation of maximum entropy distributions and thermostatistical relationships for supra-extensive entropy [21], which have not been considered so far. Presented framework could also be applied for thermostatistical analysis of another SPA entropies not considered here, such as Bekenstein-Hawking entropy [32] and superexponential entropy [33], as well as for more general group entropies [34], [22] [35], [36], [37], [38]. The framework can particularly be useful for the analysis of thermodynamic stability of SPA entropies [18], [16] which will be discussed elsewhere.…”

Section: Resultsmentioning

confidence: 99%

Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies

2019

View full text Add to dashboard Cite

The class of strongly pseudo-additive entropies, which can be represented as an increasing continuous transformation of Shannon and Rényi entropies, have intensively been studied in previous decades. Although their mathematical structure has thoroughly been explored and established by generalized Shannon-Khinchin axioms, the analysis of their thermostatistical properties have mostly been limited to special cases which belong to two parameter Sharma-Mittal entropy class, such as Tsallis, Renyi and Gaussian entropies.In this paper we present a general analysis of the strongly pseudo-additive entropies thermostatistics by taking into account both linear and escort constraints on internal energy. We develop two types of dualities between the thermostatistics formalisms. By the first one, the formalism of Rényi entropy is transformed in the formalism of SPA entropy under general energy constraint and, by the second one, the generalized thermostatistics which corresponds to the linear constraint is transformed into the one which corresponds to the escort constraint. Thus, we establish the equivalence between four different thermostatistics formalisms based on Rényi and SPA entropies coupled with linear and escort constraints and we provide the transformation formulas. In this way we obtain a general framework which is applicable to the wide class of entropies and constraints previously discussed in the literature.As an example, we rederive maximum entropy distributions for Sharma-Mittal entropy and we establish new relationships between the corresponding thermodynamic potentials. We obtain, as special cases, previously developed expressions for maximum entropy distributions and thermodynamic quantities for Tsallis, Rényi and Gaussian entropies. In addition, the results are applied for derivation of thermostatistical relationships for supra-extensive entropy, which has not previously been considered.

show abstract

“…In this case, the sample space grows sub-exponentially, W ARW ∼ 2 √ N /2 , and S ARW = (log W ARW ) 2 . The next example is the magnetic coin model (MC) [21], where each coin can be in two states: head or tail, however, two coins can also stick together and create a bond state. It can be shown that the corresponding sample space grows super-exponentially, W M C ∼ N N/2 e 2 √ N .…”

Section: Scaling Expansion Of the Volume Of Configuration Spacementioning

confidence: 99%

Information geometry of scaling expansions of non-exponentially growing configuration spaces

Korbel

Hanel

Thurner

2020

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

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 of the configuration space volume in terms of the scaling exponents of the system. These scaling exponents can, in turn, be used to define universality classes that uniquely determine the statistics of a system. Every system belongs to one of these classes. Here we derive the information geometry of scaling expansions of sample spaces. In particular, we present the deformed logarithms and the metric in a systematic and coherent way. We observe a phase transition for the curvature. The phase transition can be well measured by the characteristic length r, corresponding to a ball with radius 2r having the same curvature as the statistical manifold. Increasing characteristic length with respect to size of the system is associated with sub-exponential sample space growth is associated to strongly constrained and correlated complex systems. Decreasing of the characteristic lenght corresponds to super-exponential sample space growth that occurs for example in systems that develop structure as they evolve. Constant curvature means exponential sample space growth that is associated with multinomial statistics, and traditional Boltzmann-Gibbs, or Shannon statistics applies. This allows us to characterize transitions between statistical manifolds corresponding to different families of probability distributions.

show abstract

Statistical mechanics of exploding phase spaces: ontic open systems

Cited by 31 publications

References 25 publications

Classification of complex systems by their sample-space scaling exponents

Classification of complex systems by their sample-space scaling exponents

Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies

Information geometry of scaling expansions of non-exponentially growing configuration spaces

Contact Info

Product

Resources

About