Brief Review on the Connection between the Micro-Canonical Ensemble and the Sq-Canonical Probability Distribution.

Non-standard thermostatistical formalisms derived from generalizations of the Boltzmann-Gibbs entropy have attracted considerable attention recently. Among the various proposals, the one that has been most intensively studied, and most successfully applied to concrete problems in physics and other areas, is the one associated with the Sq non-additive entropies. The Sq-based thermostatistics exhibits a number of peculiar features that distinguish it from other generalizations of the Boltzmann-Gibbs theory. In particular, there is a close connection between the Sq-canonical distributions and the micro-canonical ensemble. The connection, first pointed out in 1994, has been subsequently explored by several researchers, who elaborated this facet of the Sq-thermo-statistics in a number of interesting directions. In the present work, we provide a brief review of some highlights within this line of inquiry, focusing on micro-canonical scenarios leading to Sq-canonical distributions. We consider works on the micro-canonical ensemble, including historical ones, where the Sq-canonical distributions, although present, were not identified as such, and also more resent works by researchers who explicitly investigated the Sq-micro-canonical connection.

Rényi's Entropy, Statistical Order and van der Waals Gas.

The notion of statistical order derives from the disequilibrium concept introduced by López-Ruiz, Mancini, and Calbet thirty years ago. In this effort, it is shown that the disequilibrium is intimately linked to the celebrated Rényi entropy. One also explores this link in connection with the van der Waals gas description.

Energetic Cost of Statistical Order-Degree Change in a Fermions' Set.

We discuss novel many-fermions thermodynamics' features. They refer to the energy cost associated to order-disorder changes. Our thermal quantum statistical scenario is controlled by suitable fermion-fermion interactions. We deal with two well-known quantum interactions that operate within an exactly solvable model. This model is able to adequately describe some aspects of fermion-dynamics, particularly level-crossings. We describe things via employment of Gibbs' canonical ensemble strictures. We show that judicious manipulation of the energy cost associated to statistical order (disorder) variations generates useful information-quantifiers. The underlying idea is that changes in the degree of order are intimately linked to level-crossings energetic costs.

Classical-Quantum Transition as a Disorder-Order Process.

We associate here the relationship between de-coherence to the statistical notion of disequilibrium with regards to the dynamics of a system that reflects the interaction between matter and a given field. The process is described via information geometry. Some of its tools are shown here to appropriately explain the process' mechanism. In particular we gain some insight into what is the role of the uncertainty principle (UP) in the pertinent proceedings.

Thermal-Statistical Odd-Even Fermions' Staggering Effect and the Order-Disorder Disjunction.

We review thermal-statistical considerations on the odd-even staggering effect (OES) in fermions. There is a well known OES in nuclear binding energies at zero temperature. We discuss here a thermal OES (finite temperatures) that establishes links with the order-disorder disjunction. The present thermal considerations cannot be found in the nuclear literature.

Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models.

Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems. In this work we explore the main features of information and information-based complexity indicators in exactly soluble many-fermion models of the Lipkin kind. Models of this kind have been extremely useful in shedding light on the intricacies of quantum many body physics. Models of the Lipkin kind play, for finite systems, a role similar to the one played by the celebrated Hubbard model of solid state physics. We consider two many fermion systems and show how their differences can be best appreciated by recourse to information theoretic tools. We appeal to information measures as tools to compare the structural details of different fermion systems. We will discover that few fermion systems are endowed by a much larger complexity-degree than many fermion ones. The same happens with the coupling-constants strengths. Complexity augments as they decrease, without reaching zero. Also, the behavior of the two lowest lying energy states are crucial in evaluating the system's complexity.

Decoherence, Anti-Decoherence, and Fisher Information.

In this work, we study quantum decoherence as reflected by the dynamics of a system that accounts for the interaction between matter and a given field. The process is described by an important information geometry tool: Fisher's information measure (FIM). We find that it appropriately describes this concept, detecting salient details of the quantum-classical changeover (qcc). A good description of the qcc report can thus be obtained; in particular, a clear insight into the role that the uncertainty principle (UP) plays in the pertinent proceedings is presented. Plotting FIM versus a system's motion invariant related to the UP, one can also visualize how anti-decoherence takes place, as opposed to the decoherence process studied in dozens of papers. In Fisher terms, the qcc can be seen as an order (quantum)-disorder (classical, including chaos) transition.

Structural Statistical Quantifiers and Thermal Features of Quantum Systems.

This paper deals primarily with relatively novel thermal quantifiers called disequilibrium and statistical complexity, whose role is growing in different disciplines of physics and other sciences. These quantifiers are called L. Ruiz, Mancini, and Calvet (LMC) quantifiers, following the initials of the three authors who advanced them. We wish to establish information-theoretical bridges between LMC structural quantifiers and (1) Thermal Heisenberg uncertainties ΔxΔp (at temperature T); (2) A nuclear physics fermion model. Having achieved such purposes, we determine to what an extent our bridges can be extended to both the semi-classical and classical realms. In addition, we find a strict bound relating a special LMC structural quantifier to quantum uncertainties.

Entropic Forces and Newton's Gravitation.

Our subject of interest here is entropic forces, as re-interpreted by Verlinde with reference to gravitation, that is, by appealing to Verlinde's conception of an entropic (statistically emergent) gravity advanced in [Physica A 2018, 511, 139]. In a canonical ensemble framework, we will deal with a non relativistic quantum scenario. In it, we perform a non-relativistic Schrödinger treatment (ST) of gravity as an entropic force and are able to detect new kinds of bounded quantum gravitational states, not previously reported. These new bound states would provide us with a novel energy-source, not taken into account as yet. The present entropic force deviates from the Newton's form only at extremely short distances. We propose, by specializing our results to gravitationally interacting bosons, a model for dark matter generation.

Useful Dual Functional of Entropic Information Measures.

There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born's proposal, of almost a hundred years ago, that the square modulus of any wave function | ψ | 2 be regarded as a probability distribution P. the usefulness of using information measures like Shannon's in this pure-state context has been highlighted in [Phys. Lett. A1993, 181, 446]. Here we will apply the notion with the purpose of generating a dual functional [ F α R : { S Q } ⟶ R + ], which maps entropic functionals onto positive real numbers. In such an endeavor, we use as standard ingredients the coherent states of the harmonic oscillator (CHO), which are unique in the sense of possessing minimum uncertainty. This use is greatly facilitated by the fact that the CHO can be given analytic, compact closed form as shown in [Rev. Mex. Fis. E 2019, 65, 191]. Rewarding insights are to be obtained regarding the comparison between several standard entropic measures.

Statistical Complexity of the Coriolis Antipairing Effect.

Using the entropic quantifier called statistical complexity, we investigate the interplay between (1) pairing interactions between fermions, can be viewed as analogous with superconductivity based on Cooper pairs; (2) rotations of the system as a whole around an axis; and (3) thermal excitations. Two different ordering processes are at work: alignment and pairing of two fermions to total spin zero. They compete among themselves and with thermal disorder. A complex physics ensues as a consequence. The existence of novel phenomena is revealed by the behavior of the statistical complexity. In particular, it is seen how order can arise out of disorder in originating high-temperature superconductivity.

Statistical Mechanics-Based Schrödinger Treatment of Gravity.

The entropic gravity conception proposes that what has been traditionally interpreted as unobserved dark matter might be merely the product of quantum effects. These effects would produce a novel sort of positive energy that translates into dark matter via E = m c 2 . In the case of axions, this perspective has been shown to yield quite sensible, encouraging results [DOI:10.13140/RG.2.2.17894.88641]. Therein, a simple Schrödinger mechanism was utilized, in which his celebrated equation is solved with a potential function based on the microscopic Verlinde's entropic force advanced in [Physica A 511 (2018) 139]. In this paper, we revisit this technique with regards to fermions' behavior (specifically, baryons).

Your perspective and my benefit: multiple lesion models of self-other integration strategies during social bargaining.

Recursive social decision-making requires the use of flexible, context-sensitive long-term strategies for negotiation. To succeed in social bargaining, participants' own perspectives must be dynamically integrated with those of interactors to maximize self-benefits and adapt to the other's preferences, respectively. This is a prerequisite to develop a successful long-term self-other integration strategy. While such form of strategic interaction is critical to social decision-making, little is known about its neurocognitive correlates. To bridge this gap, we analysed social bargaining behaviour in relation to its structural neural correlates, ongoing brain dynamics (oscillations and related source space), and functional connectivity signatures in healthy subjects and patients offering contrastive lesion models of neurodegeneration and focal stroke: behavioural variant frontotemporal dementia, Alzheimer's disease, and frontal lesions. All groups showed preserved basic bargaining indexes. However, impaired self-other integration strategy was found in patients with behavioural variant frontotemporal dementia and frontal lesions, suggesting that social bargaining critically depends on the integrity of prefrontal regions. Also, associations between behavioural performance and data from voxel-based morphometry and voxel-based lesion-symptom mapping revealed a critical role of prefrontal regions in value integration and strategic decisions for self-other integration strategy. Furthermore, as shown by measures of brain dynamics and related sources during the task, the self-other integration strategy was predicted by brain anticipatory activity (alpha/beta oscillations with sources in frontotemporal regions) associated with expectations about others' decisions. This pattern was reduced in all clinical groups, with greater impairments in behavioural variant frontotemporal dementia and frontal lesions than Alzheimer's disease. Finally, connectivity analysis from functional magnetic resonance imaging evidenced a fronto-temporo-parietal network involved in successful self-other integration strategy, with selective compromise of long-distance connections in frontal disorders. In sum, this work provides unprecedented evidence of convergent behavioural and neurocognitive signatures of strategic social bargaining in different lesion models. Our findings offer new insights into the critical roles of prefrontal hubs and associated temporo-parietal networks for strategic social negotiation.

Thermodynamics of firms' growth.

The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper, we show that a thermodynamic model based on the maximum entropy principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical framework is tested against a comprehensive database of Spanish firms, which covers, to a very large extent, Spain's economic activity, with a total of 1,155,142 firms evolving along a full decade. We show that the empirical exponent of Pareto's law, a rule often observed in the rank distribution of large-size firms, is explained by the capacity of economic system for creating/destroying firms, and that can be used to measure the health of a capitalist-based economy. Indeed, our model predicts that when the exponent is larger than 1, creation of firms is favoured; when it is smaller than 1, destruction of firms is favoured instead; and when it equals 1 (matching Zipf's law), the system is in a full macroeconomic equilibrium, entailing 'free' creation and/or destruction of firms. For medium and smaller firm sizes, the dynamical regime changes, the whole distribution can no longer be fitted to a single simple analytical form and numerical prediction is required. Our model constitutes the basis for a full predictive framework regarding the economic evolution of an ensemble of firms. Such a structure can be potentially used to develop simulations and test hypothetical scenarios, such as economic crisis or the response to specific policy measures.

Cortical dynamics and subcortical signatures of motor-language coupling in Parkinson's disease.

Impairments of action language have been documented in early stage Parkinson's disease (EPD). The action-sentence compatibility effect (ACE) paradigm has revealed that EPD involves deficits to integrate action-verb processing and ongoing motor actions. Recent studies suggest that an abolished ACE in EPD reflects a cortico-subcortical disruption, and recent neurocognitive models highlight the role of the basal ganglia (BG) in motor-language coupling. Building on such breakthroughs, we report the first exploration of convergent cortical and subcortical signatures of ACE in EPD patients and matched controls. Specifically, we combined cortical recordings of the motor potential, functional connectivity measures, and structural analysis of the BG through voxel-based morphometry. Relative to controls, EPD patients exhibited an impaired ACE, a reduced motor potential, and aberrant frontotemporal connectivity. Furthermore, motor potential abnormalities during the ACE task were predicted by overall BG volume and atrophy. These results corroborate that motor-language coupling is mainly subserved by a cortico-subcortical network including the BG as a key hub. They also evince that action-verb processing may constitute a neurocognitive marker of EPD. Our findings suggest that research on the relationship between language and motor domains is crucial to develop models of motor cognition as well as diagnostic and intervention strategies.