Hamiltonian Systems: Dynamics Through Energy Functions
Hamiltonian systems are a class of physical systems in classical mechanics that evolve according to Hamilton’s equations, which describe how
Phase Space: A Map of All Possible States
Phase space is a mathematical framework used in physics and dynamical systems to represent all possible states of a system.
Bifurcation: Sudden Shifts in System Behavior
Bifurcation refers to a qualitative change in the long-term behavior of a dynamical system that occurs when a system parameter
Strange Attractors: Fractal Patterns in Chaos
Strange attractors are intricate, fractal-like structures that appear in the phase space of chaotic dynamical systems. Unlike regular attractors (like
Chaos: Sensitivity to Initial Conditions
Chaotic systems are deterministic systems that exhibit sensitive dependence on initial conditions—a defining feature of chaos theory. This means that
Lyapunov Exponent: Measuring Chaos and Sensitivity to Initial Conditions
The Lyapunov exponent is a quantitative measure of how small differences in initial conditions grow over time in a dynamical
Non-Equilibrium Thermodynamics: Understanding Systems in Transition
Non-equilibrium thermodynamics is the branch of thermodynamics that studies systems that are not in thermal, mechanical, or chemical equilibrium. Unlike
Landauer’s Principle: The Thermodynamic Cost of Forgetting
Landauer’s Principle is a foundational concept in the physics of information, stating that erasing one bit of information in a
Boltzmann Constant: Bridging Microscopic Energy and Temperature
The Boltzmann constant (k or k₈) is a fundamental physical constant that connects the average kinetic energy of particles in
Fluctuation–Dissipation Theorem: Linking Noise to Response
The fluctuation–dissipation theorem (FDT) is a fundamental principle in statistical mechanics that connects spontaneous fluctuations in a system at equilibrium