Let the topological space S be the state space of a thermodynamic system S, define r is less than or approximately equal s if s can be attained from r by means of an adiabatic process performed on script. The results of physical experimentation show that this relation is a quasi-order. A real-valued function defined on S which preserves this order relation is called an empirical entropy function. An expository account is given of known sufficient conditions on the order relation and the state space S which guarantee the existence of a continuous empirical entropy function. A statement on the zero-th law of thermodynamics is used to establish an equivalence relation on the state space S. Sufficient conditions are given for there to exist an order relation less than or equal defined on S such that the order topology induced on S by the relation less than or equal is compatible with the original topology on S.
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- Functions (Mathematics);
- State Vectors;
- Phase Transformations;
- Thermodynamics and Statistical Physics