Molecular Dynamics Simulations: Basics and Algorithms

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Statistical Definition of Entropy: Microstates and Macrostates

Covers microstates, macrostates, entropy, and density of states in statistical mechanics.

Thermodynamic Transformations and Entropy

Explores thermodynamic transformations of ideal gases, heat capacity, entropy, and adiabatic processes.

Ensembles and Partition Functions

Covers ensembles, partition functions, and distributions in statistical thermodynamics.

Hamiltonian Formulation and Equivalence with Euler-Lagrange

Explores Hamiltonian formulation and its equivalence with Euler-Lagrange equations, illustrated through examples.

Mechanics: Equilibrium Points and Stability

Explores equilibrium points and stability in mechanical systems, analyzing how systems return to or move away from their positions after disturbances.

Thermodynamic Functions and Equilibria: Mathematical Tools

Discusses thermodynamic functions, their mathematical tools, and key relationships between state variables in thermodynamics.

Constraints and Lagrange

Covers constraints, Lagrange equations, generalized coordinates, cyclic coordinates, conservation laws, and Hamilton formalism.

Molecular dynamics: Integrating Newton's equations

Explores molecular dynamics, integrating Newton's equations to make atoms move according to interatomic forces.

Conservation of Total Energy

Explores the conservation of total energy in systems with time-independent potential energy, demonstrating its constancy and importance in verifying numerical integration accuracy.

Canonical Transformations in Analytical Mechanics

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.