The Dissipation Theory of Aging: A Quantitative Analysis Using a Cellular Aging Map

Continuous-time systems are often represented by differential equations, including Ordinary Differential Equations (ODEs) like the motion of a pendulum and Partial Differential Equations (PDEs) such as the heat equation, which describe system behavior in response to time and other variables. For systems that evolve at discrete intervals, difference equations--using linear or nonlinear recursive functions--capture state changes over time, as seen in models of population growth. Dynamical systems can also be described geometrically via phase or state space, where each point represents a system state, and trajectories represent system evolution. Alternatively, vector fields describe time evolution as a flow, mapping system states across time steps, thereby outlining the system's path on its phase space manifold. In physics, it's more common to describe the dynamical systems using Hamiltonian or Lagrangian formalisms, which provide a more structured way of capturing the energy dynamics of a system. In systems where randomness or noise plays a role, stochastic differential equations (SDEs) are used.