ON CITIES AND ENTROPY: A THERMODYNAMICAL VIEW OF THE
LARGE TOWNS
Nilo Costa Serpa
Centro
Universitário ICESP de Brasília, Brazil
E-mail: nilo.serpa@icesp.edu.br
Submission: 1/18/2019
Accept: 5/2/2019
ABSTRACT
Present article proposes the application of
the concept of entropy in the study of the environmental impacts created by a
city. It was taken a strictly thermodynamic approach of cities as heat sinks
that generate entropy. The formalism of caloric field theory was adopted to
establish the relationship between entropy caused by thermal exchanges and the
physical environmental parameters considered. The notion of evolutional global
time was 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 was
set.
Keywords: entropy; thermodynamics; irreversible processes; caloric field theory
1.
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 (2002), in his
Dictionary of Philosophy, observes that
“Há dois
conceitos técnicos de entropia diferentes e não relacionados, a saber: o físico
e o informacional. Nenhum deles é relevante para a filosofia, embora a palavra
‘entropia’ seja uma favorita entre os filósofos pops”.[1] (BUNGE, 2002).
Also,
Bunge (1973) highlights a common wrong idea:
“[…] the
interpretation of entropy as a measure of our ignorance is invalid, for it
involves the erroneous identification of statistical mechanics with
epistemology.” (BUNGE, 1973),
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” (BUNGE,
1973).
Most
of these claims are correct except for one. We 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 (BUNGE, 1973).
Undoubtedly, imaginationist and
voluntarist idealism brought ills to the study of entropy, beginning with the
association of a figurative time counted by clock-hands. From a macroscopic
point of view, everything indicates that entropy progresses gradually and
slowly from the past to the future, so that time must be treated more
adequately as an evolutional variable on a scale independent of the
conventional time of daily life.
The permanent advance of entropy makes the
spurious idealism in the notion of “negative entropy” — the misconception of
negentropy — give rise to the rational and objective concept of “entropy
deceleration”. So, what makes sense to state is that, locally, we can have
decelerated entropy and some correlated effects. 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). Entropy is a
quantity that can only grow. Its deceleration gives the impression that it has
been reversed, as each accelerating state is able, under certain circumstances,
to trigger surprisingly organized processes (for instance, frequent aerobic
exercise increases secondary vascularization, producing microvessels that
reduce the risk of fatal vascular accidents, although the aging of the organism
continues to progress, at best, to natural organ failure).
From there one can already see how much
nonsense is expected when searching the subject. Of course, this almost
universal appeal to entropy, from thermodynamics to economics, through biology
and information theory, reflects at least a feeling that it is fundamental, yet
little understood (postmodern sociologists and systemic-minded management
theorists use entropy in a way that promotes obscurantism rather than
enlightenment).
There
are two main facts that compose the misunderstandings surrounding entropy:
firstly, the more technical, concerns the distancing from its thermodynamical
origins; secondly, the more subjective, concerns the excesses of voluntarist
and imaginationist idealism. In the first case, issues are discussed by an
unqualified quorum. In the second case, speculation comes not from scientific
plausibility, but from gratuitous fiction.
Howsoever, I think the problem in
dealing with the notion of entropy comes mainly from the supremacy of the
mechanistic educational model; it is more difficult to deal with intrinsic
thermal exchanges in complex systems. For example, it is unlikely that, by
looking at a steel structure in full oxidation, one would think of the loss of
energy associated with the degeneration of steel by the action of oxygen (there
was an earlier consumption of thermal energy to produce the steel pieces, so
that oxidation equals wasted energy). Hence it seems that thermodynamics shows
itself the most complete physical science to understand that every process of
transformation entails irreversible wear and loss. So, what we are looking for
with technology is not only to perform things efficiently, but to do it
effectively, that is, with a minimum of losses, slowing the advance of the
entropy.
That supremacy of the mechanistic educational
model is not entirely fortuitous. Ironically, thermodynamics had its origins in
observations of mechanical phenomena. According to Hiebert (1981), we can say
that thermodynamics born from the discovery of an invariant correspondence
between the macroscopic movement of a body and the heat dissipated by this
movement; in other words, a correspondence between the amount of mechanical
work that disappears and the amount of heat that appears. We have here a
statement which, by the very nature of the world of external things, would lead
to an analysis of the amount of energy that cannot be used in a complete cycle
of mechanical work. It was precisely this analysis that led to the notion of
entropy.
Serious and competent authors have
defined entropy in slightly different but equivalent ways. Ultimately, we 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 of the system in question are not so evident. Depending on the scale of
the system, however, it is possible to create a thermal emissivity
representation; an urban system would be a good example.
A
great city, being the center of complex and diversified human relations, bears
a thermodynamical image if we think of the heat dissipated in traffic, civil
construction works, industrial machines, mobile telephony, human bodies,
residential lamps, public lighting, and so on. However, the main objective of
this work is to construct not a complete thermodynamical image but a starting
point for more precise researches on the control variables necessary for an
effective urban management of energy and wastes from its dissipation[2].
2.
METHODS AND APPLICATIONS
Climatology is a very complex science, so if we were to analyze urban
climatic phenomena in their particularities, we would most likely find
ourselves in trouble in a tangle of possibilities, some of which considered
controversial. Fortunately, present macroscopic approach allows us to observe
an object with middling homogeneous areas under the prism of its global thermal
emissions, something that considerably simplifies the analysis in progress.
There is
no scarcity of imagery devices to aid modern urban climate studies. With the
increasing development of satellite imagery systems, the images produced have
come to constitute an important tool for observing and analyzing climatic
phenomena, particularly with respect to urban environments. Images from the
NOAA / AVHRR satellite (spatial resolution of 1.1 km at Nadir) are applicable
to climatic studies of large urban centers, while images from the Landsat 5 and
7 satellites, with spatial resolutions of 120 and 60 meters, respectively, have
provided support to the study of configuration and thermal variation in the
intra-small size. Faced with so many resources, several authors have been
working on the theme of urban heat (GÁL; UNGER,
2014; LI et al., 2016; MIDDEL et al., 2018; ZENG et al., 2018).
The
concept of caloric field is in fact a deepening of the idea of thermal field
(SERPA et al., 2016; SERPA,
2017a; SERPA, 2017b; SERPA, 2018) with the main difference that the field, at
first non-massive[3],
is described in its evolution as being a complex scalar associated with its own
entropy by a field equation,
(1)
where is the field and
is the opacity of
the medium. In fact, this construct may be generalized to varied contexts of
thermal irradiation, although the gauging only manifests beneath an intense
field, where thermochemical transformations occur from a certain amount of
matter in interaction with the field[4].
That
equation of field evolution is deduced from a Lagrangian density whose role is
precisely to establish a coded symmetry for derivation of the equations of
“motion” of the system in question. The complex scalar representation was
chosen to ensure an always positive entropy according to the field equation;
also, it generalizes the formalism so that, when gauging is applicable, it
becomes technically useful. So, for instance, let us take the caloric field
with its conjugate
where is the
generalized coordinate,
is
the polytropic index,
is
the opacity of the medium and
is the refractive index of the medium. The polytropic
regime assumption is in fact a simplifier hypothesis[5] (SERPA, 2018). Lagrangian
density is given by
(1.a)
Application
of Noether’s theorem shows that there is a conserved caloric strength ,
(1.b)
(1.c)
Derivatives
of both fields are
and
.
Second derivative of the first field is
(2)
Substituting in field equation, it follows
(3)
This is
the expression of the opacity as a function of polytropic index and refractive
index, remembering that the range of interest of the polytropic index is
limited to . For the air, with a significant degree of humidity, we
may consider
, which is approximately the value observed in Earth's
atmosphere. Assuming the refractive index of the air equal to
and
substituting both values in expression (3), we obtain
This is
the mean Earth's atmosphere opacity in normal conditions. It is noteworthy that
field entropy, given by
(4)
is positive for any value of the field. To check this,
take the expressions
and replace in equation (4),
The
generalized coordinate is a time function, not the time of
clocks but the global evolutional time
valued
in the interval
. Within this
very small range, the growth of entropy can be excellently described by
with
By
definition, the rate of entropy variation is given by
(5)
with being
the average Sky View Factor (SVF) of the city. Since the entire lifetime of a
city is undefined, and since the global evolutional time range is very small,
we can assume that the variable
has
"now" a very small value[6]
in generic time Units (tU),
which would allow us to approximate the exponential function to 1. According to
the table furnished by Middel et al
(2018), I adapted another table with the rate of entropy for some cities in the
world (Table 1).
Table 1: Average entropy rate for some cities.
|
CITY |
SVF (average) |
AVERAGE ENTROPY RATE (J/oK.tU2) |
|
Manhattan |
0.545 |
0.016886 |
|
Paris |
0.586 |
0.019522 |
|
Singapore |
0.595 |
0.020126 |
|
Seoul |
0.680 |
0.026287 |
|
Tokyo |
0.693 |
0.027302 |
|
Vancouver |
0.713 |
0.028901 |
|
Philadelphia |
0.720 |
0.029471 |
|
Bonn |
0.746 |
0.031638 |
|
San Francisco |
0.811 |
0.037391 |
Source:
adapted by the author from Middel et al,
2018.
Thus,
the theoretical entropy accelerates as SVF increases.
3.
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 heat islands were brought by
Oke (1978, 1981, 1982, 1988), 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
,
where dTmax =
intensity of the heat island (oC) (OKE, 1982).
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
(ZENG et al, 2018).
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 (1 – γ2), 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
Substituting the derivatives,
which is obviously
true for any global time.
4. CONCLUSION
Present article showed a new
approach of urban entropy based on the concept of caloric field developed previously
in detail by the author (SERPA, 2017a, 2017b, 2018). In fact, it is a
continuation of author’s former research (SERPA et al., 2016) on the issue of
sustainable environmental management with regard to human urban waste
interactions withal, since these interactions are frequently source of
economic, health and aesthetic problems.
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.
ACKNOWLEDGMENTS
The author thanks the Pro-Rectory
of Research and Innovation of the Centro Universitário ICESP for the financial
support to this research.
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