By Christian A. Engelbrecht
Read Online or Download Quarks and leptons : proceedings of the Fourth South African Summer School in Theoretical Physics, held at the University of Stellenbosch, January 21-February 1, 1985 PDF
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Additional resources for Quarks and leptons : proceedings of the Fourth South African Summer School in Theoretical Physics, held at the University of Stellenbosch, January 21-February 1, 1985
Example text
2)). We subsequently found that the most probable energy division between system 1 and system 2 was such that the logarithmic dervatives of the two densities were equal. This allowed us to identify the most probable macrostate as the state for which system 2 has the same microcanonical temperature as the reservoir, although, strictly speaking we had little use for the concept of ‘temperature’. We can consider an alternative procedure in which the characteristics of the density of states in the heat bath are hardly mentioned.
7. (a) Lennard–Jones potential representing the interaction between two Ar atoms as a function of the distance (in a˚ ngstr¨oms) between their mass centres. (b) Approximate form of the nucleon–nucleon potential. Compared with the atomic interaction, the length scale is 105 times smaller and the energy scale 106 times larger. (ln[N ] − 1). 1) we immediately obtain the equation of state PI = − NT ∂ FI = . 2) The entropy of the ideal gas is provided by the definition S = −∂ F/∂ T . We find SI = N ln V + 3 2 ln[2πmT ] − ln[h 3 ] − (ln[N ] − 1) + 3 2 .
The averaging is carried out over all states of the combined system. This kind of relation is typical of thermodynamics and, indeed, is appropriate for many large systems for which fluctuations away from the average values can be neglected at least to first order (for a study of fluctuations see Klimontovitch [7]). In such systems it is often true that average values and most probable values are essentially identical, since the construction of the average is dominated by the most probable macrostate.