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