TABLE OF CONTENTS It is always possible to define a microscopic state of the system since, in principle, the equations of motion (quantum or classical) of the particle constituents completely define the system. Microscopic states can be defined in classical and quantum mechanics whether or not the system is in equilibrium since the equations of motion are known.
To appreciate the task of statistical mechanics, it is useful to contrast the following characteristics of the microscopic and macroscopic definitions of state:
For macroscopic systems the microscopic definition of state is extremely detailed and requires knowledge about every particle in the system. Classically, it is necessary to specify all coordinates at some particular time. In quantum mechanics, all relevant properties are computed from the wave function at a particular time, the wave function being obtained from a second-order partial differential equation involving all particle coordinates. For macroscopic systems, however, there is no way to get such detailed information, and even if it were available, it would be useless.
In thermodynamics, the macroscopic state says nothing about microscopic parameters and does not even recognize their existence. Furthermore, the macroscopic state is specified by a small number of parameters (the phase rule), in sharp contrast to the enormous number of variables that enter into the microscopic state.
The microscopic definition of state is totally causal in the sense that the state at any time is determined by the state at some earlier time. This means that all measurable quantities...
