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[[category:quantum system]] ...

...tatistical mechanics simulations, and semiempirical AM1, PM3, and PDDG/PM3 quantum mechanics (QM) calculations. The MM calculations cover energy minimizations ...

fact that the [[Helmholtz energy function]] of a system can be cast as a functional of arrives at the true Helmholtz energy of the system and the equilibrium ...

...ed: the (number) density. This classical state of affairs implies that the quantum [[De Broglie thermal wavelength |thermal de Broglie wavelength]] of the par ...nt calculations. Thus, apart from being an appealing mathematical problem, quantum hard spheres can be very useful from a practical standpoint for the design ...

...Long-Range and Short-Range Potentials - Application to a Charged Particle System", Progress of Theoretical Physics, '''50''' pp. 409-423 (1973)] ...1143/PTP.50.1156 Junzo Chihara "Integral Equations for Neutral and Charged Quantum Fluids Including Extension of the Percus-Yevick Equation" Progress of Theor ...

...inimization approach for electronic computations that scales linearly with system size", Physical Review B '''48''' pp. 14646-14649 (1993)] ...dejón, David A. Drabold, Richard M. Martin and Matthew P. Grumbach "Linear system-size scaling methods for electronic-structure calculations", Physics Review ...

...Scott Habershon, Thomas E. Markland, and David E. Manolopoulos "Competing quantum effects in the dynamics of a flexible water model", Journal of Chemical Phy ...r via [[Computation of phase equilibria#Direct simulation of the two phase system | direct coexistence]] calculations, and at 257K from calculations of the [ ...

...include [[Force fields |force-field]] based (''classical'') simulations on system ranging in complexity from simple molecular liquids (.e.g, [[water]], [[amm ...le integration techniques also developed by the principle authors. Nuclear quantum effects can be studied as well using the principle authors' [[Path integral ...

...sse. Nachrichten, pp. 1-40 (1906)]</ref>) states that the [[entropy]] of a system approaches a minimum (that of its ground state) as one approaches the [[tem [[category: quantum mechanics]] ...

====Quantum==== Silicon is a [[Polyamorphic systems | polyamorphic system]]. ...

...s that result in the observed macroscopic description of the thermodynamic system. ...so and Constantino Tsallis "Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics", Physical Review E '''78''' 021102 ( ...

...rac statistics]] and [[Bose–Einstein statistics]] for the system (i.e. the system behaves classically). ...lational [[Degree of freedom |degrees of freedom]] is negligible (i.e. the system behaves classically). ...

| System || model || <math>T_{\mathrm {TMD}}</math> (K) || density at <math>T=T_{\ma ...doi.org/10.1063/1.3239471 E. G. Noya, C. Vega, L. M. Sesé, and R. Ramírez "Quantum effects on the maximum in density of water as described by the TIP4PQ/2005 ...

*[[Quantum hard spheres]] *[[Weeks-Chandler-Andersen reference system model]] ...

...sco Paesani, Soohaeng Yoo, Huib J. Bakker and Sotiris S. Xantheas "Nuclear Quantum Effects in the Reorientation of Water",Journal of Physical Chemistry Letter ...http://dx.doi.org/10.1021/jp710640e Francesco Paesani and Gregory A. Voth "Quantum Effects Strongly Influence the Surface Premelting of Ice", Journal of Physi ...

...al and Two-dimensional Systems Possessing a Continuous Symmetry Group. II. Quantum Systems", Journal of Experimental and Theoretical Physics '''34''' pp. 610 ...l [[XY model]]. Below the transition temperature, <math>T_{KT}</math>, the system plays host to a 'liquid' of vortex-antivortex pairs that have zero total vo ...

...ng|thumb|right|Phase diagram (pressure vs packing fraction) of hard sphere system (Solid line - stable branch, dashed line - metastable branch)]] ...7 B. J. Alder and T. E. Wainwright "Phase Transition for a Hard Sphere System", Journal of Chemical Physics '''27''' pp. 1208-1209 (1957)]</ref>, much of ...