When do generalized entropies apply? How phase space volume determines entropy

We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a {\em generalized} (non-additive) form. We show that generalized entropies can only exist when the dynamically (statistically) relevant fraction of degrees of freedom in the system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen and is practically statistically inactive. Systems governed by generalized entropies are therefore systems whose phase space volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for binomial processes and argue that generalized entropies could be relevant for self organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.Comment: 5 pages, 2 figure

Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches

Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent processes. Their statistics is typically non-multinomial in the sense that the multiplicities of the occurrence of states is not a multinomial factor. The maximum entropy principle is tightly related to multinomial processes, non-interacting systems, and to the ensemble picture; it loses its meaning for path-dependent processes. Here we show that an equivalent to the ensemble picture exists for path-dependent processes, such that the non-multinomial statistics of the underlying dynamical process, by construction, is captured correctly in a functional that plays the role of a relative entropy. We demonstrate this for self-reinforcing Pólya urn processes, which explicitly generalize multinomial statistics. We demonstrate the adequacy of this constructive approach towards non-multinomial entropies by computing frequency and rank distributions of Pólya urn processes. We show how microscopic update rules of a path-dependent process allow us to explicitly construct a non-multinomial entropy functional, that, when maximized, predicts the time-dependent distribution function

The freshwater crayfish Austropotamobius pallipes in South Tyrol. Heritage species and bioindicator

Rapid decline of crayfish in European freshwaters and continuing threat necessitate integrated actions in conservation and management of native crayfish populations. Besides biological reasons (diseases, plague), the impact of toxic and harmful substances (fertilisers, herbicides) or wastewater effluents, habitat alteration or fragmentation have been responsible for their decline in some regions. The same is true for the region of South Tyrol, where compared to previous investigations, only 10 of a former total of 15 crayfish locations in the water bodies could be affirmed. Although two new populations of the non-indigenous Astacus astacus were detected, the native Austropotamobius pallipes continues to decline. While many investigations have focused accurately on causal coherences for the decline of native populations, the properties of crayfish facilitate to reverse the situation. In a few examples, the potential of Austropotamobius pallipes, the native crayfish in South Tyrol, as “surrogate species” for effective biological conservation is discussed. Given the various adequate attributes of freshwater crayfish as surrogate species (including indicator species, umbrella species and flagship species qualities), they may help to advance not only the crayfish situation itself but also freshwater ecosystem properties in general

Mars: Mariner 9 spectroscopic evidence for H2O ice clouds

Spectral features observed with the Mariner 9 Interferometer Spectrometer are identified as those of water ice. Measured spectra are compared with theoretical calulations for the transfer of radiation through clouds of ice particles with variations in size distribution and integrated cloud mass. Comparisons with an observed spectrum from the Tharsis Ridge region indicate water ice clouds composed of particles with mean radius 2.0 microns and integrated cloud mass 0.00005 g/sq cm

How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions

Sample space reducing (SSR) processes offer a simple analytical way to understand the origin and ubiquity of power-laws in many path-dependent complex systems. SRR processes show a wide range of applications that range from fragmentation processes, language formation to search and cascading processes. Here we argue that they also offer a natural framework to understand stationary distributions of generic driven non-equilibrium systems that are composed of a driving- and a relaxing process. We show that the statistics of driven non-equilibrium systems can be derived from the understanding of the nature of the underlying driving process. For constant driving rates exact power-laws emerge with exponents that are related to the driving rate. If driving rates become state-dependent, or if they vary across the life-span of the process, the functional form of the state-dependence determines the statistics. Constant driving rates lead to exact power-laws, a linear state-dependence function yields exponential or Gamma distributions, a quadratic function produces the normal distribution. Logarithmic and power-law state dependence leads to log-normal and stretched exponential distribution functions, respectively. Also Weibull, Gompertz and Tsallis-Pareto distributions arise naturally from simple state-dependent driving rates. We discuss a simple physical example of consecutive elastic collisions that exactly represents a SSR process

The Nimbus 4 Infrared Spectroscopy Experiment, IRIS-D. Part 1: Calibrated Thermal Emission Spectra

Calibrated infrared emission spectra of earth and atmosphere using high resolution interferometer spectrophotometer on Nimbus 4 satellit

The infrared interferometer spectrometer experiment for the Mars Mariner 1971 orbital mission

Infrared interferometer spectrometer for Mariner spacecraft in Mars orbi

Generalized information entropies depending only on the probability distribution

Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and $F$-distributions of $\beta$. It is assumed that they depend only on $p_l$, the probability associated with the microscopic configuration of the system. For each of the three $\beta-$distributions we calculate the Boltzmann factors and show that they coincide for small variance of the fluctuations. For the Gamma distribution it is possible to calculate the entropy in a closed form, depending on $p_l$, and to obtain then an equation relating $p_l$ with $\beta E_l$. We also propose, as other examples, new entropies close related with the Kaniadakis and two possible Sharma-Mittal entropies. The entropies presented in this work do not depend on a constant parameter $q$ but on $p_l$. For the $p_l$-Gamma distribution and its corresponding $B_{p_l}(E)$ Boltzmann factor and the associated entropy, we show the validity of the saddle-point approximation. We also briefly discuss the generalization of one of the four Khinchin axioms to get this proposed entropy.Comment: 13 pages, 3 figure

Low-Cost, Class D Testing of Spacecraft Photovoltaic Systems Can Reduce Risk

The end-to-end verification of a spacecraft photovoltaic power generation system requires light! A lowcost, portable, and end-to-end photovoltaic-system test appropriate for NASA's new generation of Class D missions is presented. High risk, low-cost, and quick-turn satellites rarely have the resources to execute the traditional approaches from higher-class (A-C) missions. The Class D approach, as demonstrated on the Lunar Atmospheric and Dust Environment Explorer (LADEE), utilizes a portable, metalhalide, theatre lamp for an end-to-end photovoltaic system test. While not as precise and comprehensive as the traditional Large Area Pulsed Solar Simulator (LAPSS) test, the LADEE method leverages minimal resources into an ongoing assessment program that can be applied through numerous stages of the mission. The project takes a true Class D approach in assessing the technical value of a costly, highfidelity performance test versus a simpler approach with less programmatic risk. The resources required are a fraction of that for a LAPSS test, and is easy to repeat due to its portability. Further, the test equipment can be handed down to future projects without building an on-site facility. At the vanguard of Class D missions, the LADEE team frequently wrestled with and challenged the status quo. The philosophy of risk avoidance at all cost, typical to Class A-C missions, simply could not be executed. This innovative and simple testing solution is contextualized to NASA Class D programs and a specific risk encountered during development of the LADEE Electrical Power System (EPS). Selection of the appropriate lamp and safety concerns are discussed, with examples of test results. Combined with the vendor's panellevel data and periodic inspection, the method ensures system integrity from Integration and Test (I&T) through launch. Following launch, mission operations tools are utilized to assess system performance based on a scant amount of available data