Infinitesimal and Heat Sink/Bath
Infinitesimal arguments are well suited to many forms of calculus. However they can lend themselves to mental hardship when irrationally applied to thermodynamics especially when they are not given proper context.
Certainly infinitesimal changes can be reversible, but such infinitesimal changes are NOT necessarily measureable i.e. too small. Moreover they are often meaningless because true reversibility generally only occurs when the infinitesimal change is zero! Or if prefer reversibility appears realistic when infinitesimal change approaches zero, hence is NOT a real process.
Moreover, if there were a sufficient/massive number (approaching infinite) number of infinitesimal changes then the change can become real. And if this change involved work. or thermal energy transfer between systems, then this becomes real change i.e. a measureable change. And processes whereby energy/work change is measureable are generally irreversible processes.
Similar voids in logic often applies to heat sink or heat baths. Herein real change often does not affect the heat sink/baths measureable parameters. In other words real energy change tends to be NOT measureable inside of heat sinks/baths. This is not to say that the change was infinitesimal although the principles are very much the same.
Again, if you had a sufficient/massive number (approaching infinite) number of real changes then the energy change to the heat sink/bath will become measureable.
And the mother of all heat baths/sinks that we deal with on a daily basis (experimentally and otherwise) is the Earth’s atmosphere and/or atmosphere plus planet.
Real processes to heat baths/sinks are logicistically similar to infintesimal
processes to real systems.
Real processes to heat baths/sinks are logicistically similar to infintesimal processes to real systems.Never forget whether thinking infinitesimal change to real systems, or real change to a heat sink/bath, that the change cannot be simply ignored unless it is zero, in which case it becomes completely meaningless.