How accurate is this brief summary of Thermodynamics? I am trying to write a sort of "universal" equation sheet that all instructors can use on closed-book exams (with minimal modification.)  Since it is not a teaching tool I can be extremely concise.  But it needs to be 100% accurate (within a certain context).  Are the following definitions valid all the time?  I used the shorter "demonic" instead of "Maxwell's demon", and assume that the sophisticated reader will understand that this holds only for the entire system
∆T=0 Isothermal  |  ∆Q=0 Adiabatic  |  ∆P=0 Isobaric
∆S=0 Reversible  |  ∆S>0 Irreversible  |  ∆S<0 Demonic
 A: You need to be clear if your "summaries" are referring to thermodynamic processes or changes in state. I will assume you mean processes.

∆T=0 Isothermal

Not necessarily if you are referring to an isothermal process. A process can result in a final equilibrium temperature equal to the original equilibrium temperature without the temperature being constant during the process. An isothermal process is one in which the system temperature is constant all during the process.

∆Q=0 Adiabatic

The $\Delta$ symbol is normally used to represent a change in state of a thermodynamic property, such as pressure, temperature, volume, internal energy, entropy, etc.. Heat, $Q$ (and work, $W$) is not a thermodynamic property, but a transfer of energy. It is more correct to describe an adiabatic process as one where $Q=0$.

∆P=0 Isobaric

Similar comment as regarding the first summary. If the pressure is constant throughout the process, the process is isobaric. A process where the initial and final equilibrium pressures are the same is not necessarily an isobaric process.

∆S=0 Reversible

This is true only if $\Delta S$ means the total change in entropy of the system plus the surroundings. $\Delta S=0$ for the system alone is a minimum necessary but not sufficient condition for a reversible process. Moreover, for a cycle $\Delta S$ of the system is zero for both a reversible and irreversible cycle.

∆S<0 Irreversible (Demonic)

$\Delta S$ can be less than zero for the system alone or the surroundings alone in a process, but never be less than zero for the combination of the system and surroundings.

As I was hoping, I knew about all but one of your caveats when I
posted. I missed the differential of heat, dQ. This is extremely
confusing to students because it is an inexact differential. I will
leave it up to the instructors to deal with these complexities, for
now. The equation sheet will be editable for instructors who use them.

Problem is, if the caveats are not included or understood by the instructors, students may not fully understand the implications of the summaries. I think you may be trying to do too much by using only $\Delta$ in each case if you are dealing with processes. If I were to try and summarize these concepts as briefly as possible with the minimum amount of additional information in parenthesis.
$T=$ constant. Isothermal process. ($T$ = system temperature)
$\delta Q=0$ or $Q=0$ Adiabatic process. ($Q$ or $\delta Q$ = total or differential amount of heat transfer).
$P$ = constant. Isobaric process. ($P$ = system pressure*)
$\Delta S_{Tot}=0$ Reversible process. ($\Delta S_{Tot}=\Delta S_{sys}+\Delta S_{sur}$)
$\Delta S_{Tot}>0$ Irreversible process
$\Delta S_{Tot}<0$ Impossible. (For a process, $\Delta S_{sys}<0$ or $\Delta S_{sur}<0$ is possible)
(*Caveat- For irreversible process $P$ is the external pressure, not the gas pressure, since the system is not in internal equilibrium during the  process.)
Hope this helps.
