If we had only a single lecture in statistical thermodynamics

To provide an outline of the topics discussed in the book, I present a summary of the salient concepts of statistical thermodynamics in the following section. 

The overarching goal of classical statistical thermodynamics is to explain thermodynamic properties of matter in terms of atoms. Briefly, this is how  

Consider a system with N identical particles contained in volume V with a total energy E. Assume that N,V, and E are kept constant. We call this an NVE system (Fig. 1.1). These parameters uniquely define the macroscopic state of the system, that is all the rest of the thermodynamic properties of the system are defined as functions of N, V, and E. For example, we can write the entropy of the system as a function S = S(N,V, E), or the pressure of the system as a function p = P N, V, E). Indeed, if we know the values of N, V, and E for a single-component, single-phase system, we can in principle find the values of the enthalpy H, the Gibbs free energy G, the Helmholtz free energy A, the chemical potential jx, the entropy S, the pressure P, and the temperature T. In Appendix B, we sununarize important elements of thermodynamics, including the fundamental relations between these properties. 

A fundamentally important concept of statistical thermodynamics is the microstate of a system. We define a microstate of a system by the values of the positions and velocities of all the N particles. We can concisely describe a microstate with a 6A-dimensional vector 

are the three position coordinates and ti are the three velocity coordinates of particle i, respectively, with i = 1,2,N. By definition, r, = dr /dt. Note that the positions and the velocities of atoms do not depend on one another. 

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