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As far as my understanding goes, the only reversible heat engine is the Carnot engine, described by the Carnot cycle. On the other hand, in all of the resources I've found the change in entropy for reversible (quasi-static?) processes is defined as $ds=\frac{dq}{T}$. That includes isochoric and isobaric quasi static process, right? Then how come, for say an engine compromised of a cycle of three reversible process: isochoric, isothermal and isobaric, that the engine itself is not reversible?

I know that the change in entropy (of the entire isolated system, AKA the engine and the temprature reservoirs) is not zero, but still. If each process is considered reversible in itself, how come that it's impossible to reverse the entire process by reversing each of them individually, one after the other?

I'm getting quite desperate, honestly. Is it just a disambiguation of the term "reversible"? Is an isochoric process not reversible, but just quasi static?

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    $\begingroup$ The "Carnot cycle" is one very specific reversible cycle consisting of four stages: isothermal-adiabatic-isothermal-adiabatic. There are other kinds of reversible cycles that are associated with other thermodyanic variables not necessarily constant at any of it legs. $\endgroup$ – hyportnex Jul 16 '17 at 14:56
  • $\begingroup$ isochoric means that the volume is constant during the process that can be reversible or irreversible, quasi-static or not quasi-static. For further study read Fermi (easier) or Pippard (more difficult) $\endgroup$ – hyportnex Jul 16 '17 at 14:57
  • $\begingroup$ Actually, if the cycle is reversible, the change in entropy of the entire isolated system, consisting of the engine and temperature reservoirs, is zero. $\endgroup$ – Chet Miller Jul 16 '17 at 15:00
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If a given system passes through a continuous sequence of thermodynamic equilibrium states during a process, then the process is called "internally reversible" for that system. If a given system and each external system that it interacts with (comprising the surroundings) all pass through a continuous sequence of thermodynamic equilibrium states during the process, then the process is regarded as "fully reversible." Under these circumstances, both the system and the surroundings can be returned to their initial states without causing a significant change in anything else. So an internally reversible process has the credentials for also being a fully reversible process, and will be part of a fully reversible process provided the surrounding also undergo reversible paths.

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