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The canonical ensemble

The canonical ensemble. Q = -Q R. Consider system at constant temperature and volume. adiabatic wall. System . Heat Reservoir R. T=const. We have shown in thermodynamics that system with (T,V)=const . in equilibrium is at a minimum of the Helmholtz free energy, F.

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The canonical ensemble

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  1. The canonical ensemble Q = -QR Consider system at constant temperature and volume adiabatic wall System  Heat Reservoir R T=const. We have shown in thermodynamics that system with (T,V)=const. in equilibrium is at a minimum of the Helmholtz free energy, F (T=const, V=const.)

  2. We use a similar approach now in deriving density function and partition function System can exchange energy with the heat reservoir: Find maximum of S under the constraint that average (internal) energy is given under constraints found by maximizing Using again Lagrange multiplier technique

  3. Partition function of the canonical ensemble with Next we show @ V,N constant From the constraint With the equilibrium distribution back into the entropy expression

  4. With and @ V,N constant Using we find With Gives meaning to the Lagrange parameter

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