Statistical mechanics

Statistical mechanics (or statistical thermodynamics^[1]) is the application of probability theory (which contains mathematical tools for dealing with large populations) to study the thermodynamic behavior of systems of a large number of particles. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level.

It provides a molecular-level interpretation of macroscopic thermodynamic quantities such as work, heat, free energy, and entropy, allowing the thermodynamic properties of bulk materials to be related to the spectroscopic data of individual molecules. This ability to make macroscopic predictions based on microscopic properties is the main advantage of statistical mechanics over classical thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy. However, entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.

Statistical mechanics (or statistical thermodynamics) was born in 1870 with the work of Austrian physicist Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.^[2] Boltzmann's original papers on the statistical interpretation of thermodynamics, the H-theorem, transport theory, thermal equilibrium, the equation of state of gases, and similar subjects, occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. The term "statistical thermodynamics" was proposed for use by the American thermodynamicist and physical chemist J. Willard Gibbs in 1902. According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish physicist James Clerk Maxwell in 1871.

Statistical mechanics

Statistical thermodynamics Kinetic theory [show]Particle Statistics Maxwell-Boltzmann Bose-Einstein · Fermi-Dirac Parastatistics · Anyonic statistics Braid statistics [show]Ensembles Microcanonical · Canonical Grand canonical Isothermal–isobaric Isoenthalpic–isobaric [show]Thermodynamics Gas laws · Carnot cycle · Dulong-Petit [show]Models Debye · Einstein · Ising [show]Potentials Internal energy · Enthalpy Helmholtz free energy Gibbs free energy [show]Scientists Maxwell · Gibbs · Boltzmann

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Classical mechanics

Newton's Second Law

History of ... [hide]Branches Statics · Dynamics / Kinetics · Kinematics · Applied mechanics · Celestial mechanics · Continuum mechanics · Statistical mechanics [show]Formulations Newtonian mechanics Lagrangian mechanics Hamiltonian mechanics [show]Fundamental concepts Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle [show]Core topics Rigid body · Rigid body dynamics · Motion · Newton's laws of motion · Newton's law of universal gravitation · Equations of motion · Inertial frame of reference · Non-inertial reference frame · Rotating reference frame · Fictitious force · Displacement (vector) · Relative velocity · Friction · Simple harmonic motion · Harmonic oscillator · Vibration · Damping · Damping ratio · Rotational motion · Circular motion · Uniform circular motion · Non-uniform circular motion · Centripetal force · Centrifugal force · Centrifugal force (rotating reference frame) · Reactive centrifugal force · Coriolis force · Pendulum · Rotational speed · Angular acceleration · Angular velocity · Angular frequency · Angular displacement [show]Scientists

Of thermodynamics, in 1949, Albert Einstein said "A theory is the more impressive the greater the simplicity of its premises are, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of applicability of its basic concepts, it will never be over-thrown."