By Biryukov O.N.
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Extra resources for A bound for the topological entropy of homeomorphisms of a punctured two-dimensional disk
0. 44) is the analytical statement of the second law of thermodynamics, ﬁrst given by Clausius in 1862. It was on this basis that he ﬁrst postulated the existence of a new state function—entropy. For adiabatic systems, the entropy remains constant if the process is reversible The second law of thermodynamics and always increases if the process is irreversible. The entropy continues to increase until the system reaches equilibrium. This necessarily implies that equilibrium is the state of maximum entropy.
It is, however, 45 46 Thermodynamic theory of solutions of limited utility without a supplemental description of the behavior of speciﬁc solutions. This supplemental description cannot be derived from thermodynamics.
57) implies: Wnon-mechanical ÀdA À pdV ¼ Àd(A þ pV): In this case, it is convenient to introduce a new state function, the Gibbs free energy, deﬁned as G ¼ A þ pV ¼ U À TS þ pV ¼ H À TS: (1:59) For isobaric-isothermal processes, Wnon-mechanical ÀdG: (1:60) In order to prevent a spontaneous process from proceeding, we must do some work on the system. Obviously, this work must exceed the nonmechanical work that the system performs during the spontaneous process. Therefore, the non-mechanical work can be used to determine whether a spontaneous process will occur: Wnon-mechanical !
A bound for the topological entropy of homeomorphisms of a punctured two-dimensional disk by Biryukov O.N.