06 Nov 2023
Macroeconomic dynamics in a finite world based on thermodynamic potential
LIED —
Université Paris Cité, 35 rue H. Brion, 75013 Paris
Author
Eric Herbert ,
Gael Giraud,
Aurélie Louis Napoléon
and Christophe Goupil
contacts:
eric.herbert@u-paris.fr , christophe.goupil@u-paris.fr ,
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| Top, physical sheets with four sectors interconnected by a central kernel. |
| Bottom, global structure of a sheet of resource. Left part is the production area, middle part is forced recycling, and right part is natural recycling. |
In this work we are interested in the connection between economic spheres and physical resources. Rather than integrating thermodynamic formalism into economic modeling, we create a generic tool for describing the use of a resource as a function of its availability (the volume of its stock) and the intensity of its use, based on the concepts of quantity and quality.
Abstract of the paper
This paper presents a conceptual model describing the medium and long term co-evolution of natural and socio-economic subsystems of Earth. An economy is viewed as an out-of-equilibrium dissipative structure that can only be maintained with a flow of energy and matter. The distinctive approach emphasized here consists in capturing the economic impact of natural ecosystems’ depletion by human activities via a pinch of thermodynamic potentials. This viewpoint allows: (i) the full-blown integration of a limited quantity of primary resources into a non-linear macrodynamics that is stock-flow consistent both in terms of matter-energy and economic transactions; (ii) the inclusion of natural and forced recycling; (iii) the inclusion of a friction term which reflects the impossibility to produce (and recycle)goods and services without exuding energy and matter wastes, and (iv) the computation of the anthropically produced entropy as a function of metabolizing intensity and frictions. Analysis and numerical computations confirm the role played by intensity and frictions as key factors for sustainability by contrast with real gdp growth—as well as the interplay between resource scarcity, income inequality, and inflation. A more egalitarian society with moderate inflation turns out to be more sustainable than an unequal society with low inflation. Our approach is flexible enough to allow for various economic models to be embedded into our thermodynamic framework. Finally, we propose the open source EcoDyco software as a first complete realization implementing economic dynamics in a multi-resource environment.
To know more about it, see
Herbert, É., Giraud, G., Louis-Napoléon, A., & Goupil, C. (2023). Macroeconomic dynamics in a finite world based on thermodynamic potential. Sci. Rep., 13(18020), 1–27. doi
15 Oct 2023
Power Production in living systems: a biomimetic model of
optimisation constrained by resource management
LIED —
Université Paris Cité, 35 rue H. Brion, 75013 Paris
contacts:
eric.herbert@u-paris.fr ,
christophe.goupil@u-paris.fr ,
patrick.laurenti@u-paris.fr
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| Two morphotypes of the same species, Astyanax mexicanus. On the top the blind and depigmented cave morphotype, on the bottom the surface morphotype. |
Master internship
We propose a master internship at the interface of physics and biology, supervised by biologist and
physicist, to study the adaptation of the power production mechanism of
animals to the environment.
Power production
The power production mechanism, for example dedicated to locomotion, is a general and vital process
based in the animal world on the degradation of ATP molecules during the
Krebs cycle. However, this common process, far from freezing the
modalities of use and power production of living systems, adapts to the
specific environmental constraints encountered by each population.
More specifically, we are interested, in a biomimetic approach, in the
adaptive optimisation of energy conversion systems according to the
constraints imposed on access to resources.
To this end, we are developing a theoretical and experimental approach,
deriving the well-known formalism of non-equilibrium thermodynamics
to living systems and relying on the description of biological
mechanisms of metabolism, and in particular oxygen consumption. This
allows us to reconstruct the energy flows through the organism and to
characterise it quantitatively using generic parameters allowing
inter-individual comparison.
Although our approach has so far focused mainly on mammalian species (in
particular the horse, see ref below), the development of simple
metabolic characterisation tools allows us to consider broadening the
range of species studied. Following preliminary work carried out in the
laboratory, we have designed a device (swimming tube and sensors) to
record the consumption of dioxygen of actinopterygian fish. In order to
limit the effects due to genetic variability, we propose to compare
morphotypes of the same species. We have chosen Astyanax mexicanus, a
species in which there are two separate but interbreeding populations: a
surface morphotype, a predator with a very vivacious behaviour, and a
cavernicolous morphotype, a detritivore with a placid behaviour. In
addition, we propose to conduct a phylogenetic analysis that will allow
us to describe the evolution of biological processes that determine the
ability to produce and sustain effort in all vertebrate animals; and, in
particular, to characterise the evolution of mechanisms of adaptation to
effort during the transition from aquatic to terrestrial life in the
vertebrate lineage as a bioinspired model of adaptive transition.
To know more about it, see
Herbert et al. Thermodynamics of Animal Locomotion. Physical Review
Letters 125, 22 (2020): 228102.
https://doi.org/10.1103/PhysRevLett.125.228102
Goupil et al. Thermodynamics of metabolic energy conversion under muscle load, New J.
Phys., vol. 21 (2019),
https://iopscience.iop.org/article/10.1088/1367-2630/ab0223
[— Possibility of continuing to a PhD —]
15 Nov 2020
This paper is a foundation of thermodynamics of animal locomotion. It builds on previous paper that discussed the metabolic behaviour (here) of living system and the notion of adaptability for living organism (here)
Author
E. Herbert, H. Ouerdane, Ph. Lecoeur, V. Bels and Ch. Goupil
Download
The paper was accepted on November 2020 in Phys. Rev. Lett.. For the moment, it can be found on Phys. Rev. Lett. website
Abstract
Muscles are biological generators of mechanical power. They have been extensively studied in the frame of Hill’s classic empirical model as isolated biomechanical entities, which hardly applies to a living body subjected to internal and environmental constraints. Here we elucidate the overarching principle of a \emph{living} muscle action for a specific purpose such as locomotion, considering it as an assembly of chemical-to-mechanical energy converters (muscle units) connected in parallel, under mixed boundary conditions. Introducing the energy cost of effort, COE−, as the generalization of the well-known oxygen cost of transport, COT, in the frame of our compact locally linear non-equilibrium thermodynamics model, we analyze oxygen consumption measurement data from a documented experiment on energy cost management and optimization by horses moving at three different gaits. Horses adapt to a particular gait by mobilizing a nearly constant number of muscle units minimizing waste production per unit distance covered; this number significantly changes during transition between gaits. The mechanical function of the animal is therefore determined both by its own thermodynamic characteristics and by the metabolic operating point of the system.
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| *Top: experimental data and
obtained fit with the proposed modeling.
On top is plotted the oxygen flux \(\Phi_{O_{2}}\)
while in the middle plot is presented \(COT \equiv \Phi_{O_ {2}}/v\) (which depends on the speed of displacement) respectively for walk (red stars), trot (blue circles) and gallop (green squares).
The dotted curves are the fit obtained from the model.
Left: experimental data from\,\cite{Hoyt1981} (horse B) and
obtained fit with the proposed modeling.
On top is plotted the oxygen flux \(\Phi_{O_{2}}\)
while in the middle plot is presented \textit{COT}\(\equiv \Phi_{O_ {2}}/v\) (which depends on the speed of displacement) respectively for walk (red stars), trot (blue circles) and gallop (green squares).
The dotted curves are the fit obtained from the model.
Note (in inset) the COT dramatic increase for the high velocity walk: this slope change marks the change of regime in this region (these points were not used for curve fit, see text.)
On the Bottom, on top is plotted \(N_0\varphi_{-}/M\) while at the bottom is plotted specific COT\(/M\) and based on \(v/v^{*} \propto i_M\); \(M = 140kg\) is the mass of the horse. In both cases, the thick dark line is a 2-parameter fit of the aggregated data (see text). All gaits are considered as a collection of a different number of activated muscle units.
In inset is shown the relative value of \(N\), \({N_0}/{N}\).
The walk was chosen as a reference gait (\(X_ {0}\)); \({v_ {0}^{*}}/{v^{*}}\) is represented
in \(\bullet\) blue, \({B_{v0}}/{B_{vb}}\) in red \(+\), and
\({R_ {vb}}/{R_ {v0}}\) with dark \(\star\).
The line \(1/v^{*}\) (red dotted line) has been drawn as a guide for the eyes for comparison purposes.
Note (in inset) the COT dramatic increase for the high velocity walk: this slope change marks the change of regime in this region (these points were not used for curve fit, see text.)
On the right, on top is plotted \(N_0\varphi_{-}/M\) while at the bottom is plotted specific COT\(/M\), and based on \(v/v^{*} \propto i_M\); \(M = 140kg\) is the mass of the horse. In both cases, the thick dark line is a 2-parameter fit of the aggregated data (see text). All gaits are considered as a collection of a different number of activated muscle units.
In inset is shown the relative value of \(N\), \({N_0}/{N}\).
The walk was chosen as a reference gait (\(X_ {0}\)); \({v_ {0}^{*}}/{v^{*}}\) is represented
in \(\bullet\) blue, \({B_{v0}}/{B_{vb}}\) in red \(+\), and
\({R_ {vb}}/{R_ {v0}}\) with dark \(\star\).
The line \(1/v^{*}\) (red dotted line) has been drawn as a guide for the eyes for comparison purposes. * |
15 Oct 2020
Approche thermodynamique hors d’équilibre de la production de puissance dans les systèmes vivants
Contacts eric.herbert@univ-paris-diderot.fr et christophe.goupil@univ-paris-diderot.fr
Localisation Université de Paris, 35 rue H. Brion, 75013 Paris
Nous proposons un sujet de stage et/ou de thèse sur les thématiques de l’équipe.
Le sujet complet est disponible ici
La mesure de l’oxygène comme indicateur métabolique est une technique robuste largement répandue dans les
centres hospitaliers et sportifs, comme dans les laboratoires sur différents organismes. Elle est ici mise à profit pour renseigner le flux de
déchet énergétique issu de la conversion de l’énergie chimique en énergie mécanique. Ces mesures de flux d’oxygène,
divisées par la vitesse de déplacement du sujet (humain ou animal), déterminent le COT. Cette grandeur est
directement associée à la production de déchet métabolique durant un effort unitaire, tel qu’une unité de longueur
parcourue par exemple. Des travaux récents nous ont permis de valider l’ensemble de cette approche de modélisation
en l’appliquant au cas du cheval, qui présente l’intéressante particularité de posséder plusieurs allures de déplacement
A ce jour aucune modélisation n’a permis de rassembler l’ensemble de ces résultats dans un même cadre. Nous
proposons donc d’utiliser ce modèle pour rendre compte de la variabilité de ces paramètres dans une classe
d’individus homogène d’une part et de l’évolution de ces paramètres en fonction de l’âge d’autre part.
Le programme scientifique prévu se compose d’un axe expérimental et un d’axe théorique qui se dérouleront en parallèle :
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Axe théorique.
En s’appuyant sur les travaux menés au laboratoire , développement du formalisme associé aux transitoires et à la prise en compte de la totalité de l’impédance musculaire (active et réactive)
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Axe expérimental.
\((i)\) mise en place et le déroulement de protocoles de mesures stationnaires, \((ii)\) développement d’un système permettant une mesure instantanée, incluant les transitoires, de l’impédance de sortie mécanique d’un sujet à l’effort.
- En collaboration avec l’APHP et l’INSEP: étude du COT à la marche et à la course en fonction de la vitesse et de l’inclinaison chez l’humain.
- En collaboration avec le Museum d’Histoire Naturelle, étude du COT chez l’animal
- Développement d’un vélo instrumenté pour mesures d’impédance de sortie mécanique.
