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Let $S= (s_1

We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of available resources. A symmetry phase transition takes place at Gini values 1/3, where realistic distributions become asymmetric. Four constraints act on S: expectedly, N and W, and new ones, diversity and interactions between individuals; the latter result from the two coordinates of a single point in the data, the peak. The occupation number of a job is either zero or one, suggesting Fermi-Dirac statistics for employment. Contrariwise, an indefinite nujmber of individuals can occupy a state defined as a quantile of income or of age, so Bose-Einstein statistics may be required. Indistinguishability rather than anonymity of individuals and resources is thus needed. Interactions between individuals define define classes of equivalence that happen to coincide with acceptable definitions of social classes or periods in human life. The entropy S is non-extensive and obtainable from data. Theoretical laws are compared to data in four different cases of economical or physiological diversity. Acceptable fits are found for all of them., Comment: 13 pages, 2 figures

Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences.

We describe a core system for autonomous navigation in outdoor natural terrain. The system consists of three parts: a perception module which processes range images to identify untraversable regions of the terrain, a local map management module which maintains a representation of the environment in the vicinity of the vehicle, and a planning module which issues commands to the vehicle controller. Our approach is to use the concept of 'early traversability evaluation', and on the use of reactive planning for generating commands to drive the vehicle. We argue that our approach leads to a robust and efficient navigation system. We illustrate our approach by an experiment in which a vehicle travelled autonomously for one kilometer through unmapped cross-country terrain.