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Statistical thermodynamics 3-1. Irreversibility and Equilibrium "5 of isolated system in equilibrium 5 depends on "constraint" which are specified by some macroscopic parameters (external parameters and any other conditions in 2-2.), {y1, y2, ... ,yn} (eg. yi=V, H, E, ...) = # of accessible states with (i = 1, ... , n) "removal of some constraint # of accessible states must increase or be unchanged. In the final equilibrium situation, systems in ensemble are distributed over all possible 5f states. If , it is very unlikely that the initial distribution of systems is restored after removal of constraints. [its probability ] Consider only one parameter y. With constraint n y, initially y=yi. After removal of constraint, y can take any value. Usually, 5(y) has very pronounced maximum at some value . a4 In final equilibrium situation, practically all systems will have values of y very close to . <If some constraints of an isolated system are removed, the parameters tend to readjust themselves to minimize > "irreversibility " a4 redistribution of systems in ensemble until 5f states are equally likely. By putting back constraints on the system, the systems cannot return to initial distributions over 5i states only. (eg. free exp.) a4 irreversible process and, during the process, the system is in non-equilibrium "a4 no redistributions of systems and all states are always equally likely. a4 during the process, the system is always in equilibrium and reversible process. 3-2 Thermal interactions (1)Entropy and temperature Consider two macroscopic system A and A' which are initially separated in equilibrium and isolated. Suppose their respective mean energies are = Ei and ' = Ei'. Then, make thermal contacts between them so that energies can be exchanged. 6 equilibrium property : isolated system. : constant. (*weak interaction assumptions : negligible ) What value does E assume in equilibrium ? Let = # of accessible states of when A has an energy between . ^