Microcanonical temperature definition

Since we have confirmed that the phase space volume can be practically calculated as above (see Appendix B for an illustrated example of such a numerical example), we now make use of it to define a microcanonical temperature. A useful alternative definition of Vst( ) is a convolution type... 

The definition of entropy and the identification of temperature made in the last subsection provides us with a coimection between the microcanonical ensemble and themiodynamics. 

By definition, the microcanonical ensemble contains all possible configurations in the 6N-dimensionaI phase space with the same energy and a constant probability of being in each configuration N is the number of particles in the system under consideration. This ensemble describes an isolated system with constant N and V, or constant N and zero external pressure [28]. Constant-energy simulations are not recommended for equilibration because, without the energy flow facilitated by the temperature control methods, the desired temperature cannot be achieved. However, during the data collection phase, if one is... 

When the Boltzmann distribution was derived in Section 5.2, we assumed a constant number of particles (N) and a given volume (V). We also assumed that the energy was constant. In the canonical ensanble, we imagine that the subsystems (members of the canonical ensemble) may exchange energy but not particles with each other. The ensemble that we are supposed to use is the one where the assumptions agree with the experimental conditions. Since the total energy is constant in the microcanonical ensemble, the definition of such a simple concept as temperature has to be done indirectly. 

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