On power law
Power-Law Scaling in Fundamental Processes In this work, I explore how power-law scaling naturally emerges from the interactions of fundamental processes, specifically in the context of how time and physical systems are interrelated. I introduce a process formalism, emphasizing relational flow dynamics over traditional notions of state and time. This approach reveals that power-law scaling governs the behavior of these processes. 1. Process Formalism To understand the evolution of systems, we define the process tensor , which describes the relationship between two flows: P μ ν = ∂ μ ϕ ν − ∂ ν ϕ μ P_{\mu\nu} = \partial_\mu \phi_\nu - \partial_\nu \phi_\mu Here, ϕ ν \phi_\nu represents the process field . This tensor captures the interaction between processes, which are not static but evolve relative to each other. This allows us to move beyond the idea of states and focus on dynamic interactions. 2. Conservation Law and Evolution The fundamental conservation of the system is capt...