This chapter explores the intricate dynamics between medium-sized and large enterprises in EU candidate countries through the lens of Bohm's interpretation of Bohr's complementarity principle and Heisenberg's uncertainty principle which are two fundamental concepts in quantum theory. By drawing parallels between quantum mechanics and economic behavior, the research posits that the growth trajectories of these enterprises are interrelated, exhibiting complementary relationships under uncertainty that reflect the principles of quantum duality. Employing a robust research methodology, the chapter presents empirical evidence showcasing the correlation between capital concentration and growth rates of medium-sized and large enterprises across various regions. Statistical analyses, including Pearson coefficients, reveal significant relationships that support the hypothesis of a higher share of medium enterprises correlating with an increased presence of large enterprises revalidating complementariness. Furthermore, the findings highlight important policy implications for regional economic development, emphasizing the need for tailored strategies that foster the growth of both enterprise sizes under uncertain conditions. By integrating quantum theory with economic dynamics, this chapter contributes a novel perspective to the discourse on entrepreneurship and regional growth, encouraging further exploration of interdisciplinary approaches in econophysics research.
This chapter explores the intricate dynamics between medium-sized and large enterprises in EU candidate countries through the lens of Bohm's interpretation of Bohr's complementarity principle and Heisenberg's uncertainty principle which are two fundamental concepts in quantum theory. By drawing parallels between quantum mechanics and economic behavior, the research posits that the growth trajectories of these enterprises are interrelated, exhibiting complementary relationships under uncertainty that reflect the principles of quantum duality. Employing a robust research methodology, the chapter presents empirical evidence showcasing the correlation between capital concentration and growth rates of medium-sized and large enterprises across various regions. Statistical analyses, including Pearson coefficients, reveal significant relationships that support the hypothesis of a higher share of medium enterprises correlating with an increased presence of large enterprises revalidating complementariness. Furthermore, the findings highlight important policy implications for regional economic development, emphasizing the need for tailored strategies that foster the growth of both enterprise sizes under uncertain conditions. By integrating quantum theory with economic dynamics, this chapter contributes a novel perspective to the discourse on entrepreneurship and regional growth, encouraging further exploration of interdisciplinary approaches in econophysics research.
Abstract Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a novel approach by transposing fundamental concepts of quantum mechanics—such as superposition, operator algebra, and path integrals—into the realm of macroeconomic modeling. Within this quantum framework, core economic variables (capital, labor, and technological progress) are redefined as non-commuting operators acting on Hilbert spaces, and the state of the economy is represented as a dynamic wave function governed by a time-dependent Hamiltonian. The evolution of this economic wave function follows a generalized Schrödinger equation, developed here through Dyson series and Magnus expansions. We also define a quantum production function as the expected value of a composite operator, capturing the probabilistic nature of economic output. By integrating uncertainty relations analogous to Heisenberg's principle, and modeling economic fluctuations via Langevin dynamics, we extend the model to include dissipation, feedback loops, and non-linear interactions between variables. Finally, a Feynman path integral formalism is constructed to provide an alternative trajectory-based interpretation of economic dynamics. This quantum-inspired framework offers a rigorous and flexible methodology to rethink macroeconomic modeling under radical uncertainty, with potential applications in dynamic policy simulations and innovation-driven growth.
Quantum economics is an interdisciplinary field that combines the principles of quantum mechanics and economic theories. The research examines the main theoretical and practical aspects of quantum economics, starting with its theoretical foundations based on the principles of quantum mechanics, such as superposition, uncertainty and entanglement, and ending with practical applications and perspectives for further research. Special attention was paid to the potential impact of quantum technologies on finance, marketing, supply chain management, as well as on macroeconomic planning and policy. It discusses how quantum algorithms can transform traditional approaches in economic research and practice, providing new methods for analyzing complex data, improving forecasting of economic trends, and optimizing decisions under uncertainty. Quantum economics opens up new perspectives for understanding dynamic and interconnected processes in the global economy, which can fundamentally change our perception of economic laws and strategies. It is emphasized that the quantum economy is at the initial stage of its development, and scientists and practitioners face many challenges and questions that need to be solved. In the future, we can expect the development of new tools for economic analysis and decisionmaking based on quantum computing, which will allow us to cope with current and future economic challenges more effectively. The quantum economy can also offer new approaches to risk management and financial security, especially in light of growing cyber threats and the need to protect economic information. Quantum economics is an exciting and promising direction that can significantly enrich both theoretical and applied aspects of economic science.
Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical evolution of the concept of complementarity, beginning with Bohr's original formulation. It then explores its modern quantification through complementarity relations and its profound connection to the foundational postulates of quantum theory. Furthermore, it delves into key related developments, such as the operational definition of complementarity in the context of incompatible observables, its potential links with quantum uncertainty relations and contextuality, its various applications, and other pertinent topics. This review aims to serve physicists interested in quantum resources, quantum correlations, and the foundational principles of quantum mechanics.
This study examines how David Bohm’s quantum theoretical principles, embodied in wholeness, implicate order, and holomovement provide innovative frameworks for reconceptualizing sustainable development. Current approaches remain constrained by mechanistic paradigms that fragment economic, environmental, and social systems, limiting transformative solutions to recurring global crises. Through systematic conceptual analysis and cross-disciplinary literature review, this research develops consciousness-based models that transcend fragmented thinking and separated domains by applying quantum metaphysical principles in socio-economic systems in an integrated manner. Comparative systems analysis reveals significant parallels between quantum mechanical principles and economic behavior, demonstrating how Bohm’s framework addresses sustainability challenges through the epistemological and ontological transformation of information rather than mere technical optimization. Generalization and illustrative modeling show how implicate order dynamically enables economic coherence, organizational intelligence, and systemic governance. Expressions are derived for unfolding sustainable development operators and kinematic transformations evolving with quantum economics. Two central quantities emerge: active and passive information, exhibiting close analogies with gravitational pull and sustainability potential, bounded by thermodynamic laws and entropy principles. This formulation corresponds to and transcends the quantum law of syllogism, bridging information theory, quantum mechanics, and sustainability metrics. The 2025 coherence–entropy sustainable development scores findings correlatively unify Shannon entropy, Bohmian coherence, and Feynman extremals. A sustainability law of syllogism was suggested, confirming the systemic coherence of the scores. The Appendix validates Bohm’s concepts, facilitating paradigm shifts from mechanistic control to participatory transformation, establishing theoretical foundations for quantum-informed economics, consciousness-based management, and holistic responses to global sustainability challenges that have become increasingly urgent since Bohm’s original discoveries.
To address the practical impasse of mainstream economics—rooted in the deterministic worldview of Newtonian mechanics—where its mechanistic and linear analytical framework struggles to handle complex scenarios in the digital economy era, such as interactive decision-making, globally non-local correlations, and systemic mutations after sudden shocks, leading to a pronounced tension between theory and practice, this paper constructs a quantum economics analytical framework. Drawing on the inherent uncertainty revealed by quantum mechanics and based on the core isomorphism between economic systems and quantum systems (both centering on uncertainty, featuring superposition of multiple states, observer-induced interaction, and holistic correlations), it translates quantum core logics like superposition, entanglement, and transition into economic analytical tools. Methods such as entanglement entropy and quantum state transition probabilities are employed to quantify the complex correlations and state transformations of economic variables. Empirical studies of China’s macroeconomy validate the framework’s effectiveness, precisely capturing structural features like the strong correlation between money supply and economic growth, transmission frictions between money and prices, and paradigm shifts under policy shocks and event impacts. It further reveals the synergistic effect of a multi-variable system (“1+1+1>3”), quantifies the transitional characteristics and transformation laws of inflation states. The findings demonstrate that quantum economics elevates “uncertainty” to the theoretical core, transcending the paradigm limitations of traditional economics. It provides a novel quantitative perspective for understanding the complex essence and structural contradictions of economic systems, offering a systematic solution to the challenges of modern economic complexity.
Abstract Since Adam Smith, economics has erected a grand edifice upon the foundations of rational agents, equilibrium analysis, and linear causality; however, the 2008 global financial crisis, the European sovereign debt crisis, and the COVID-19 pandemic have successively revealed its fundamental limitations when confronted with complex economic phenomena: bubbles that ought not to have existed, crises unforeseen by equilibrium models, non-linear ruptures brought about by technological revolutions, and self-fulfilling expectations—all of which call for a richer theoretical language. This book serves as the foundational introduction to the "Quantum Economics Textbook Series," as well as the first gateway into this entire series. It introduces the methodological framework, mathematical apparatus, and philosophical insights of quantum mechanics to economic analysis, grounding its approach in the core proposition of a practical ontology—that human economic practice itself possesses quantum attributes such as superposition, entanglement, constructibility, uncertainty, and emergence—thereby reconstructing the economic world as a quantum process of superposition and evolution. Six core concepts—superposition, entanglement, measurement collapse, the uncertainty principle, quantum transitions, and emergence—run throughout the work. Quantum economics does not represent a simple negation of classical theory; rather, it constitutes a dialectical sublation: under the classical limit—where decoherence is complete, the measurement basis is fixed, and entanglement vanishes—quantum theory precisely reduces to classical theory. This book comprises five parts and thirty chapters: Part I establishes the paradigm shift and theoretical framework, covering critiques of Newton's worldview, the quantum worldview, a foundational conceptual framework, mathematical foundations, and research methodologies; Part II reconstructs quantum microeconomic theory, encompassing consumers, producers, pricing, markets, the wave-particle duality of markets, quantum games, and welfare economics; Part III builds quantum macroeconomic theory, addressing national income accounting, money, inflation, economic cycles, policy, and open economies; Part IV explores quantum finance and market dynamics, including asset pricing, portfolio management, market sentiment, risk management, and trading theory; Part V extends the scope to organizations, innovation, institutions, development, economic ethics, and the digital economy, while offering insights into the future of this discipline. This volume is intended for undergraduate and graduate students, as well as researchers in economics and related fields, and serves as the essential first volume in the quantum economics series.