On the Thermodynamics of Urban Environments The Thermal Potential of the Cities

Present article proposes the application of the concept of entropy in the study of the environmental impacts generated by a city. It is taken a strictly thermodynamic approach of cities as heat sinks that generate entropy. The formalism of caloric field theory is adopted to establish the relationship between entropy caused by thermal exchanges and the physical environmental parameters considered. The notion of evolutional global time is introduced in order to treat entropy more objectively in the context of thermodynamics. A table with the rates of change of entropy in some cities is generated.


Introduction
The concept of entropy is one of the least understood and at the same time one of the most evoked in sciences, pseudo-sciences and semi-sciences. Bunge [2]. Also, Bunge highlights a common wrong idea: "[…] the interpretation of entropy as a measure of our ignorance is invalid, for it involves the erroneous identification of 1 There are two different and unrelated technical concepts of entropy, namely: the physical and the informational. None of them is relevant to philosophy, although the word 'entropy' is a favorite among pop philosophers. (author's free translation).
statistical mechanics with epistemology" [1], and he continues saying that it is abusive to "[…] reduce entropy increase to loss of human information about the system, for this deprives statistical mechanics and thermodynamics of objectivity" [1]. Most of these claims are correct except for one. I would agree with Bunge on the lack of value of the concept of entropy for philosophy if he had not repeated the misconception of negentropy [1]. The fact is that there is no "negative entropy", but rather "entropy deceleration" (just as it does not make sense to speak of negative movement, but acceleration and deceleration can understand it as 1) the magnitude that quantifies the thermodynamical degradation of a system, and 2) the quantity that describes the incapacity of a system to process (convert) energy. Hence it is seen that remote associations of entropy with degenerating systems must go through thermodynamics, albeit indirectly, but not by mere formal analogies.
It is true that all human activity on the planet consumes energy. The problem is how to formalize this consumption in terms of the second law of thermodynamics, when the theoretical physical aspects  The concept of caloric field is in fact a deepening of the idea of thermal field [10,11,12,13] with the main difference that the field is described in its evolution as being a complex scalar associated with its own entropy by a field equation,  [13]. Lagrangian density is given by 2 In the theory of caloric fields, the gauge field is closely linked to the appearance of the so-called "minimal thermal mass factor of dynamic interaction", which responds by a massive feedback to the original field due to the thermochemical interaction between field and matter under high temperatures. 3 To the real conditions of the troposphere of Earth corresponds the state with the polytropic thermal stratification. I assume that the whole atmosphere has a polytropic stratification (vertically finite).   This is the mean Earth's atmosphere opacity in normal conditions. It is noteworthy that field entropy, given by  (Table 1). 4 In fact, it is possible to relate clock time t to via Green's functions, but this is not the case to do this in present paper.

Discussion
Measuring the field we can evaluate the entropic trail that it leaves, and so, comparing different trails among distinct climatologically similar cities, we can establish a parameter of weighting indicative of the volume of irreversible processes that affect the environment in the immediate vicinity of each city.
Note that the advancement of entropy was analyzed here only in terms of assumed natural environmental conditions. Both the refractive index and the opacity of the medium may vary significantly for anthropogenic reasons, thus affecting the rate of change of entropy. In this way, caloric field is only understood in its interaction with matter insofar as the only thing observed is the degradation of the system, not the entropy, not even the degradation of the field itself.
In present study, the concept of heat island was implicit in the entire large city. Important contributions in modeling local islands of heat were brought by Oke [6,7,8,9], among which the relation between height-distance of buildings that led to the use of the above referred technique known as the SVF, expressed through the equality max dT = 15.27 -13.88 × SVF, where dTmax = intensity of the heat island ( o C) [8].
According to this formula, the author argues that the island of heat is increased or reduced because of the loss or heat gain of the radiation by the "obstruction index" of the sky. The SVF is still widely used today as one of the most efficient urban spatial indicators for radiation and thermal environmental assessment [14].
The obstruction index is similar to the blurring γ-factor (opacity) of the medium in the former caloric field theory. In the original equation of the caloric field, the quantity 2 1 , named "luminothermic capacity", acts on the field to express the influence of the environment. The opacity may be considered both from the point of view of the radiation that arrives from an external source, and from the radiation returned to the medium from a diffusing source heated on the terrestrial surface.
Lastly, it's interesting to note that conserved caloric strength implies To verify, let us substitute the derivatives,

Conclusion
Present article showed a new approach of urban entropy based on the former concept of caloric field developed by Serpa (2016). From the field equation, considering only thermal effects of solar radiation on the urban environment, it was possible to give a satisfactory relation between the refractive index and the opacity of the medium, from which entropy and its rate of growth were obtained. Both opacity and refractive index largely mirror the level of local pollution. Also, the work discussed a global time variable as the most adequate to treat entropy, since the conventional lifetime of a city is undefined. It is hoped that this approach shall win adepts to improve the model with inclusion of anthropogenic parameters in order to build a more complete representation that helps studies in environmental economics and urban ecology. It is also expected that the model shall be applied to Brazilian cities. CALIBRE -Revista Brasiliense de Engenharia e Física Aplicada, ISSN 2526-4192. Livre direito de cópia de acordo com os princípios estabelecidos pela Creative Commons.