The chapter discusses the Thermodynamics of Mind framework, which aims to quantify the hierarchical organization of the brain and its underlying mechanisms. The brain must efficiently orchestrate distributed computation across space and time to survive and thrive, requiring hierarchical organization that facilitates fast information transfer at minimal metabolic cost. Thermodynamics, a successful framework for characterizing hierarchy in complex systems, is proposed as a natural way to quantify brain hierarchy. This framework has provided novel insights into the changing hierarchy of brain states, such as during movie watching, where the brain hierarchy is flatter than during rest. The chapter highlights the importance of understanding how hierarchical processing is driven in different brain states and the challenges in defining these states. It also explores the role of thermodynamics in understanding the brain's hierarchical organization, including the concept of irreversibility and the "arrow of time." The Thermodynamics of Mind framework has been applied to various brain states, including wakefulness, sleep, and anesthesia, and has shown promise in revealing the causal mechanisms of brain dynamics. The chapter concludes by discussing future research avenues, including the use of turbulence and the fluctuation-dissipation theorem to better understand brain function and the potential of the framework in predicting treatment outcomes for neuropsychiatric disorders.The chapter discusses the Thermodynamics of Mind framework, which aims to quantify the hierarchical organization of the brain and its underlying mechanisms. The brain must efficiently orchestrate distributed computation across space and time to survive and thrive, requiring hierarchical organization that facilitates fast information transfer at minimal metabolic cost. Thermodynamics, a successful framework for characterizing hierarchy in complex systems, is proposed as a natural way to quantify brain hierarchy. This framework has provided novel insights into the changing hierarchy of brain states, such as during movie watching, where the brain hierarchy is flatter than during rest. The chapter highlights the importance of understanding how hierarchical processing is driven in different brain states and the challenges in defining these states. It also explores the role of thermodynamics in understanding the brain's hierarchical organization, including the concept of irreversibility and the "arrow of time." The Thermodynamics of Mind framework has been applied to various brain states, including wakefulness, sleep, and anesthesia, and has shown promise in revealing the causal mechanisms of brain dynamics. The chapter concludes by discussing future research avenues, including the use of turbulence and the fluctuation-dissipation theorem to better understand brain function and the potential of the framework in predicting treatment outcomes for neuropsychiatric disorders.