Strongly correlated electron systems, such as transition metal oxides (TMOs), exhibit complex electronic behavior due to the interplay of multiple degrees of freedom—spin, charge, lattice, and orbital. These systems display inhomogeneous states, with competing phases leading to phenomena like colossal magnetoresistance (CMR) and high-temperature superconductivity (HTSC). The presence of quenched disorder and phase competition results in nanoscale structures and complex phase diagrams, which challenge traditional reductionist approaches. These systems are analogous to complex systems in soft matter and biology, where emergent properties arise from interactions among many components. TMOs, such as manganites and cuprates, show inhomogeneous electronic states at the nanoscale, with competing phases leading to unique properties. For example, manganites exhibit CMR due to the coexistence of ferromagnetic and antiferromagnetic phases, while cuprates show complex behaviors like stripe phases and charge-ordering. These systems are not only important for fundamental physics but also have potential applications in electronics and materials science. The complexity of these systems arises from the interplay of multiple degrees of freedom and the emergence of new properties from phase competition. This complexity is not just a result of disorder but also of the nonlinear interactions among electrons and lattice. Theoretical models and experimental studies have shown that these systems can exhibit giant responses to small perturbations, making them highly sensitive to external conditions. The study of these systems has led to a broader understanding of complexity in physics, with implications for both fundamental research and technological applications. The interplay of spin, charge, lattice, and orbital degrees of freedom in TMOs leads to a wide range of phenomena, including superconductivity, magnetoresistance, and exotic ground states. These systems are also relevant to other areas of physics, such as quantum critical phenomena and biological systems, where complexity and emergent behavior are key features. The research on strongly correlated electron systems highlights the importance of complexity in understanding and predicting the behavior of materials. The development of new theoretical models and experimental techniques is essential for unraveling the intricate relationships between different degrees of freedom and their collective behavior. This research not only advances our understanding of fundamental physics but also opens up new possibilities for technological applications in electronics and materials science.Strongly correlated electron systems, such as transition metal oxides (TMOs), exhibit complex electronic behavior due to the interplay of multiple degrees of freedom—spin, charge, lattice, and orbital. These systems display inhomogeneous states, with competing phases leading to phenomena like colossal magnetoresistance (CMR) and high-temperature superconductivity (HTSC). The presence of quenched disorder and phase competition results in nanoscale structures and complex phase diagrams, which challenge traditional reductionist approaches. These systems are analogous to complex systems in soft matter and biology, where emergent properties arise from interactions among many components. TMOs, such as manganites and cuprates, show inhomogeneous electronic states at the nanoscale, with competing phases leading to unique properties. For example, manganites exhibit CMR due to the coexistence of ferromagnetic and antiferromagnetic phases, while cuprates show complex behaviors like stripe phases and charge-ordering. These systems are not only important for fundamental physics but also have potential applications in electronics and materials science. The complexity of these systems arises from the interplay of multiple degrees of freedom and the emergence of new properties from phase competition. This complexity is not just a result of disorder but also of the nonlinear interactions among electrons and lattice. Theoretical models and experimental studies have shown that these systems can exhibit giant responses to small perturbations, making them highly sensitive to external conditions. The study of these systems has led to a broader understanding of complexity in physics, with implications for both fundamental research and technological applications. The interplay of spin, charge, lattice, and orbital degrees of freedom in TMOs leads to a wide range of phenomena, including superconductivity, magnetoresistance, and exotic ground states. These systems are also relevant to other areas of physics, such as quantum critical phenomena and biological systems, where complexity and emergent behavior are key features. The research on strongly correlated electron systems highlights the importance of complexity in understanding and predicting the behavior of materials. The development of new theoretical models and experimental techniques is essential for unraveling the intricate relationships between different degrees of freedom and their collective behavior. This research not only advances our understanding of fundamental physics but also opens up new possibilities for technological applications in electronics and materials science.