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            <title xml:lang="en">Microstates: Do outsiders worth ?</title>
            <title xml:lang="fr">Micro-états: Sont-ils importants ?</title>
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              <p>This note addresses the relevance of rare events in system dynamics, inspired by Jill North reflections on the origin of the arrow of time in thermodynamics. After identifying the existence of rare events, characterized by a Pareto distribution, within a simple gas particle simulation, we investigate their impact on entropy evolution. These rare events are associated with microstates that locally decrease entropy, in contrast to the overall entropy increase observed in the bulk of the system. We present numerical simulations of gas particles, both without and with a gravity-like attractive force, to explore the fate of these rare events. Our results show that, while rare events can transiently generate local decreases in entropy, global entropy may continue to increase in accordance with the second law of thermodynamics. The introduction of gravity-like attraction stabilizes these low-entropy configurations, allowing them to persist longer. This study highlights the interplay between rare statistical fluctuations and macroscopic thermodynamic behavior, providing new insights into the emergence and stability of order in complex systems.</p>
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              <p>Cette note aborde la pertinence d'événements rares dans la dynamique des systèmes, en s’inspirant des réflexions de Jill North sur l’origine de la flèche du temps en thermodynamique. Après avoir identifié l’existence d’événements rares, caractérisés par une distribution de Pareto, dans une simulation simple de particules de gaz, nous étudions leur impact sur l’évolution de l’entropie. Ces événements rares sont associés à des micro-états qui diminuent localement l’entropie, contrairement à l’augmentation globale de l’entropie observée dans la majeure partie du système. Nous présentons des simulations numériques de particules de gaz, sans et avec une force d’attraction de type gravitationnel, afin d’explorer le devenir de ces événements rares. Nous proposons que, bien que ces événements rares puissent générer temporairement des diminutions locales de l’entropie, l’entropie globale peut continuer à croître conformément à la seconde loi de la thermodynamique. L’introduction d’une attraction de type gravitationnel stabilise ces configurations à faible entropie, leur permettant de persister plus longtemps. Cette étude met en lumière l’interaction entre les fluctuations statistiques rares et le comportement thermodynamique macroscopique, apportant un nouvel éclairage sur l’émergence et la stabilité de l’ordre dans les systèmes complexes.</p>
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