Reversible vs. pseudostatic processes

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A reversible process is defined as one where a system can return to its initial state without any net change in the environment, while a pseudostatic process maintains thermal equilibrium through slow changes. Quasistatic processes are a subset of pseudostatic processes that can be reversed by slight adjustments to external factors. The discussion highlights that the concept of pseudostatic is tied to the time scale of changes relative to the system's internal dynamics. It is noted that in thermodynamic contexts, reversible and pseudostatic notions apply to processes like heating and gas expansion, where internal dynamics can adjust to maintain equilibrium. The relationship between these processes is crucial for understanding thermodynamic behavior in various systems.
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I wonder whether a reversible process has to be quasistatic or at least
pseudostatic? (probably there exist some processes involving magnetic field
which are reversible but not pseudostatic).

Below I define what I mean by a reversible, quasistatic and pseudostatic process.

Reversible process - let's consider a process R in which initial state of the system
was a, initial state of the environment was b and final state of the system and
environment was a' and b' appropriately. If there exists a process which
changes the state of full system (considered system + environment)
form (a',b') to (a,b) the process R is said to be reversible.

Pseudostatic process - this is a process during which it may be
assumed that both the system and its surroundings maintain thermal equilibrium
(the changes are made sufficiently slow).

Quasistatic process - this is such a pseudostatic process that in any moment
if we slightly change some of the external factors which cause it (pressure,
magnetic field, ...) we can reverse its direction.

Thanks for any answers.
 
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So, I think the notion of 'pseudostatic' is in the context of a time scale slow relative to the internal dynamics of the system. This is a thermodynamic concept, so you cannot talk about whether changes in magnetic fields are reversible or pseudostatic, because in that case you are presumably only considering a single degree of freedom. Heating materials, allowing gases to expand, (de)magnetizing ferromagnets- in these systems the notion of reversible and pseudostatic is applicable, because as you change the bulk thermodynamic properties (T, rho, M respectively), the internal dynamics of the system allow the multitude degrees of freedom of adjust accordingly to 'catch up' with these bulk changes and come back into equilibrium. This usually is not so slow, so a pseudostatic process is quite fast by human time scales.
 
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