This dissertation delves into using entropy, a fundamental concept in thermodynamics and information theory, for analyzing social dynamics. Entropy relies on a probability distribution over states, which is crucial for quantifying social systems’ complexity, unpredictability, and self-organization behavior. Through an interdisciplinary approach encompassing social physics, agent-based modeling, and sentiment analysis, the research investigates the role of entropy and its underlying probability distribution in three key areas: residential segregation, financial systems, and sentiment fluctuations in online social networks. By integrating entropy-based models that leverage the probability distribution over states, the research aims to enhance the understanding of complex social phenomena and provide practical insights for policymakers, urban planners, and social media ex- parts. The findings demonstrate the potential of entropy as a unifying framework for studying social sciences, economics, and digital social systems, highlighting the growing relevance of probability distributions in decoding patterns of social dynamics. The dissertation contributes to the theoretical basis for modeling and predicting the complexity of social networks using entropy and its associated probability distribution, with significant implications for various domains.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / As aplicaÃÃes da mecÃnica estatÃstica no estudo do comportamento humano coletivo nÃo sÃo uma novidade. No entanto, nas Ãltimas dÃcadas vimos um aumento enorme do interesse no estudo da sociedade usando a fÃsica. Nesta tese, utilizando tÃcnicas da fÃsica, nÃs estudamos leis de escala nÃo-lineares em sistemas sociais. Na primeira parte da tese realizamos a anÃlise de dados e modelagem de eleiÃÃes pÃblicas. Mostramos que o nÃmero de votos de um candidato escala nÃo-linearmente com o dinheiro gasto na campanha. Para nossa surpresa, a correlaÃÃo revelou uma relaÃÃo de escala sublinear, o que significa que o "preÃo" mÃdio de um voto cresce à medida que o nÃmero de votos aumenta. Usando um modelo de campo mÃdio descobrimos que a nÃo-linearidade emerge da concorrÃncia e a distribuiÃÃo de votos à causalmente determinada pela distribuiÃÃo do dinheiro gasto na campanha. AlÃm disso, mostramos que o modelo à capaz de prever razoavelmente o nÃmero final de votos vÃlidos atravÃs de um argumento heurÃstico simples. Por fim, apresentamos o nosso trabalho sobre alometria de indicadores sociais. NÃs mostramos como homicÃdios, mortes em acidentes de carro e suicÃdios crescem com a populaÃÃo das cidades brasileiras. Diferentemente de homicÃdios (superlinear) e eventos fatais em acidentes de carro (isomÃtrico), encontramos um comportamento sublinear entre o nÃmero de suicÃdios e a populaÃÃo de cidades, o que revela uma possÃvel evidÃncia de influÃncia social na ocorrÃncia de suicÃdios. / The applications of statistical mechanics in the study of collective human behavior is not a novelty. However, in the past few decades we shaw a huge spike of interest on the study of society using physics. In this thesis we explore nonlinear scaling laws in social systems using physical techniques. First we perform data analysis and modeling applied to elections. We show that the number of votes of a candidate scales nonlinear with the money spent at the campaign. To our surprise, the correlation revealed a sublinear scaling, which means that the average âpriceâ of one vote grows as you increase the number of votes. Using a mean-field model we find that the sublinearity emerges from the competition and the distribution of votes is causally determined by the distribution of money campaign. Moreover, we show that the model is able to reasonably predict the final number of valid votes through a simple heuristic argument. Lastly, we present our work on allometric scaling of social indicators. We show how homicides, deaths in car crashes, and suicides scales with the population of Brazilian cities. Differently from homicides (superlinear) and fatal events in car crashes (isometric), we find sublinear scaling behavior between the number of suicides and city population, which reveal a possible evidence for social influence on suicides occurrences.

Konsens ist entscheidend für viele Aspekte unseres täglichen Lebens. Von der Sprache über soziale Normen bis hin zu den Regeln eines einfachen Kartenspiels ist breite Übereinstimmung erforderlich, um den jeweiligen Zweck zu erfüllen. Auch die Meinungen zu den zentralen Themen unserer Zeit sollten so weit übereinstimmen, dass wichtige Herausforderungen gemeinsam in Angriff genommen werden können. Dies ist jedoch häufig nicht der Fall. Sowohl politische Meinungen als auch Einstellungen zu ethischen Fragen sind oft tief gespalten. Die Ursprünge einer solchen Meinungspolarisierung haben die Soziologie lange Zeit vor ein Rätsel gestellt, da soziale Einflüsse uns oft näher zusammenzubringen scheinen. Was müssen wir also annehmen, um Meinungsspaltungen zu erklären? Wann wird ein Konsens gebildet? Und welche Rolle könnte die gestiegene Kommunikation zwischen Menschen bei diesen Prozessen spielen? In dieser Arbeit werden wir uns solchen Fragen mit Hilfe mathematischer Modellierung und der Analyse sozialer Daten nähern. Im Speziellen soll dazu beigetragen werden, die Lücke zwischen mikroskopischen Annahmen über den sozialen Einfluss und der Bildung von makroskopischen Meinungszuständen in sozialen Netzwerken zu schließen. / Consensus is key for many aspects of our daily lives. Concepts ranging from language, to social norms, to the rules of a simple card game require population-scale agreement to fulfil their function. People's opinions on major issues of our time should also be reasonably consistent such that important challenges can be tackled collectively. However, this is often not the case. Political opinions as well as the attitudes towards ethical issues are often deeply divided. The origins of such opinion polarization have puzzled sociology for a long time, as social influence often seems to bring us closer together. Hence, what do we have to assume in order to explain opinion cleavages? When will consensus be formed? And what might be the role of increased communication among people in these processes? In this thesis, we tackle such questions by means of mathematical modeling and the analysis of social data. More specifically, we aim to contribute to bridging the gap between microscopic assumptions about social influence and the formation of macroscopic opinion states in social networks.

Background – Under the acceleration in globalising tendencies of monopoly capitalism aided by social hyper-connectivity and a supply of cheap international labour, fashion companies struggle to find sufficient agency to manoeuvre their way out of the unsustainable, self-inflicted problems. Since fashion companies' rhetoric on sustainability matters is often far ahead of corporate action, it requires further development and engagement by all actors. Purpose – The purpose is to investigate motivational bases for the engagement in sustainability development (SD) among employees and review the compatibility between management control systems (MCSs) in order to incentivise sustainable behaviour. Methodology – With the Design Thinking approach as baseline, a single case study design is guided by both the resource-based view as well as institutional theory to explore individuals’ motivation for engaging in SD and identify MCS misalignment inefficiencies from a bottom-up perspective. Primary data is sought through semi-structured interviews with employees of the case company, which is complemented by secondary data documents and a conceptual framework grounded in literature. The data is analysed qualitatively and quantitatively through iterative coding cycles in MAXQDA. Findings – The data not only reveals the relative importance of different determining variables of sustainable behaviour at three institutional context levels of analysis, but also allows for their categorisation into behavioural progressions in engaging in SD. Even though varying motivational bases respond to different external stimuli depending on the personal interest in sustainability topics, findings on misalignment inefficiencies point towards informal MCSs requiring reinforcement by formal MCSs. Here, a lack of knowledge or perceived incompatibility with conventional business practices hamper transformational change in SD. Implications – The single case study implies that even though dominant cultural controls have institutionalised sustainability awareness among employees, the fashion SME needs to support the engagement of employees in SD with strong sustainability leadership showing courage behind conviction and assigning clear responsibilities as well as a personal purpose to the corporate sustainability missions. Additionally, MCSs need to be set up that allow for an enhanced learning culture and increase the flow of ideas even beyond corporate walls. Since findings are limited to the single case study as well as to its institutional context, this research refers to general implication of institutional theory with resource-dependent arguments as suggested by Oliver (1997) to incentivise the engagement of employees in SD. Originality– The novelty of the work lies within the Design Thinking approach, as employee profiles on progressive behaviour for engaging in SD are theorised and crucial MCSs incentivising these specific motivational bases are derived for the case company. In addition, the ideation process leads to the theoretical establishment of an incentivisation network in which social relationships between departments are rewarded that enable collaboration, creativity and productivity in favour of SD based on Social Physics.