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/snip/Not all springs obey Hooke's law. There exists such a thing as a constant-force spring, where the force is independent of x. Such things are an article of commerce; ...In contrast, a Hooke's-law spring is less than ideal, because the force changes as a function of x. The same concepts apply to the other terms on the RHS of equation [1]. An ideal heat bath maintains a constant temperature, independent of S. Now ... an important term has been left out of equation [1]. It would be better to write dE = T dS - P dV - F dx + (voltage) d(charge) .... etc. [2] The fourth term on the RHS can be taken as an implicit /definition/ of voltage, much as the first and second terms can be (and often are) taken as implicit definitions of temperature and pressure. Again the same concepts apply. An ideal battery, by definition, maintains a constant voltage at its terminals, independent of how much charge goes in or out. It is profoundly analogous to an ideal anvil, and to an ideal heat bath. Consider the following statements: "An ideal tensioner maintains a displacement and a force." "An ideal heat bath maintains a certain entropy and temperature." «A battery maintains a charge separation and a potential difference.» The first time I see a statement like that I just assume it is a typo and laugh it off. However, when somebody makes a concerted effort to defend such a statement, I say wow, we are dealing with some serious misconceptions. /snip/