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Reversible: The change is slow enough so that the system is in a sequence of equilibrium states, in a sense strong enough to ensure entropy never increases at any time because no equilibrium recovery is needed. (I recommend reading a good book of statistical physics to understand why)

Quasistatic: The change is slow enough so that the system is in a sequence of equilibrium states, in the weak sense that the macro-variables are mostly defined (temperature, pressure… are uniform almost everywhere in the system) and that formulas about equilibrium states can be used along the path (such as $dU=TdS-PdV$, $PV=Nk_B T$... ). In this case, equilibrium “catches up” with macroscopic changes but there is still an underlying entropy creation because of equilibrium recovery.

In some cases, you may describe a progressive process as a continuous path in the space of equilibrium states, but it may not necessarily be a true succession of equilibrium states. It is slow enough to draw a continuous path, but it hides a fine-grained disequilibrium. An example is vibrating a piston at supersonic speed to progressively increase the temperature of a gas. This will look like a continuous path of equilibrium states $(V,T)$ but it hides a fine-grained disequilibrium. Another good example is a succession of small free expansions. These transformation are quasistatic but they are not reversible.

For ideal gases, examples are a bit "extreme" because equilibrium happens very fast and using a piston is a rather "smooth" action. You need violent actions to drive it out of equilibrium. When friction or viscosity is involved, even an (apparently) very slow action is irreversible.

Both definitions start by “the change is slow enough so that the system is in a sequence of equilibrium states” and this is very confusing. In the literature (most often), “quasistatic” means what I just defined except (sometimes) when the text focuses on explaining what reversibility/irreversibility is and here, writers may use the word quasistatic to mean slow, which in this context means reversible.

Reversible: The change is slow enough so that the system is in a sequence of equilibrium states, in a sense strong enough to ensure entropy never increases at any time because no equilibrium recovery is needed. (I recommend reading a good book of statistical physics to understand why)

Quasistatic: The change is slow enough so that the system is in a sequence of equilibrium states, in the weak sense that the macro-variables are mostly defined (temperature, pressure… are uniform almost everywhere in the system) and that formulas about equilibrium states can be used along the path (such as $dU=TdS-PdV$, $PV=Nk_B T$... ). In this case, equilibrium “catches up” with macroscopic changes but there is still an underlying entropy creation because of equilibrium recovery.

In some cases, you may describe a progressive process as a continuous path in the space of equilibrium states, but it may not necessarily be a true succession of equilibrium states. It is slow enough to draw a continuous path, but it hides a fine-grained disequilibrium. An example is vibrating a piston at supersonic speed to progressively increase the temperature of a gas. This will look like a continuous path of equilibrium states $(V,T)$ but it hides a fine-grained disequilibrium. Another good example is a succession of small free expansions. These transformation are quasistatic but they are not reversible.

Elementary thermodynamics uses an ideal gas with a piston as an example most of the time, examples are a bit "extreme" or "artificial" because equilibrium happens very fast and using a piston is a rather smooth action. You need violent actions to drive the system out of equilibrium. When friction or viscosity is involved, even an (apparently) very slow action is irreversible. Heat exchange at finite temperature difference is another good example of irreversible quasistatic process but possibly confusing because the requirement of being quasistatic "the system is at equilibrium at all stages" is arguably not met.

Both definitions start by “the change is slow enough so that the system is in a sequence of equilibrium states” and this is very confusing. In the literature (most often), “quasistatic” means what I just defined except (sometimes) when the text focuses on explaining what reversibility/irreversibility is and here, writers may use the word quasistatic to mean slow, which in this context means reversible.

Reversible: The change is slow enough so that the system is in a sequence of equilibrium states, in a sense strong enough to ensure entropy never increases at any time because no equilibrium recovery is needed. (I recommend reading a good book of statistical physics to understand why)

Quasistatic: The change is slow enough so that the system is in a sequence of equilibrium states, in the weak sense that the macro-variables are mostly defined (temperature, pressure… are uniform almost everywhere in the system) and that formulas about equilibrium states can be used along the path (such as $dU=TdS-PdV$, $PV=Nk_B T$... ). In this case, equilibrium “catches up” with macroscopic changes but there is still an underlying entropy creation because of equilibrium recovery.

In some cases, you may describe a progressive process as a continuous path in the space of equilibrium states, but it may not necessarily be a true succession of equilibrium states. It is slow enough to draw a continuous path, but it hides a fine-grained disequilibrium. An example is vibrating a piston at supersonic speed to progressively increase the temperature of a gas. This will look like a continuous path of equilibrium states $(V,T)$ but it hides a fine-grained disequilibrium. Another good example is a succession of small free expansions. These transformation are quasistatic but they are not reversible.

For ideal gases, examples are a bit "far fetched" because equilibrium happens very fast and using a piston is a rather "smooth" action. You need violent actions to drive it out of equilibrium. When friction or viscosity is involved, even an (apparently) very slow action is irreversible.

Both definitions start by “the change is slow enough so that the system is in a sequence of equilibrium states” and this is very confusing. In the literature (most often), “quasistatic” means what I just defined except (sometimes) when the text focuses on explaining what reversibility/irreversibility is and here, writers may use the word quasistatic to mean slow, which in this context means reversible.

Reversible: The change is slow enough so that the system is in a sequence of equilibrium states, in a sense strong enough to ensure entropy never increases at any time because no equilibrium recovery is needed. (I recommend reading a good book of statistical physics to understand why)

Quasistatic: The change is slow enough so that the system is in a sequence of equilibrium states, in the weak sense that the macro-variables are mostly defined (temperature, pressure… are uniform almost everywhere in the system) and that formulas about equilibrium states can be used along the path (such as $dU=TdS-PdV$, $PV=Nk_B T$... ). In this case, equilibrium “catches up” with macroscopic changes but there is still an underlying entropy creation because of equilibrium recovery.

In some cases, you may describe a progressive process as a continuous path in the space of equilibrium states, but it may not necessarily be a true succession of equilibrium states. It is slow enough to draw a continuous path, but it hides a fine-grained disequilibrium. An example is vibrating a piston at supersonic speed to progressively increase the temperature of a gas. This will look like a continuous path of equilibrium states $(V,T)$ but it hides a fine-grained disequilibrium. Another good example is a succession of small free expansions. These transformation are quasistatic but they are not reversible.

For ideal gases, examples are a bit "extreme" because equilibrium happens very fast and using a piston is a rather "smooth" action. You need violent actions to drive it out of equilibrium. When friction or viscosity is involved, even an (apparently) very slow action is irreversible.

Both definitions start by “the change is slow enough so that the system is in a sequence of equilibrium states” and this is very confusing. In the literature (most often), “quasistatic” means what I just defined except (sometimes) when the text focuses on explaining what reversibility/irreversibility is and here, writers may use the word quasistatic to mean slow, which in this context means reversible.

Reversible: The change is slow enough so that the system is in a sequence of equilibrium states, in a sense strong enough to ensure entropy never increases at any time because no equilibrium recovery is needed. (I recommend reading a good book of statistical physics to understand why)

Quasistatic: The change is slow enough so that the system is in a sequence of equilibrium states, in the weak sense that the macro-variables are mostly defined (temperature, pressure… are uniform almost everywhere in the system) and that formulas about equilibrium states can be used along the path (such as $dU=TdS-PdV$, $PV=Nk_B T$... ). In this case, equilibrium “catches up” with macroscopic changes but there is still an underlying entropy creation because of equilibrium recovery.

In some cases, you may describe a progressive process as a continuous path in the space of equilibrium states, but it may not necessarily be a true succession of equilibrium states. It is slow enough to draw a continuous path, but it hides a fine-grained disequilibrium. An example is vibrating a piston at supersonic speed to progressively increase the temperature of a gas. This will look like a continuous path of equilibrium states $(V,T)$ but it hides a fine-grained disequilibrium. Another good example is a succession of small free expansions. These transformation are considered as quasistatic but they are not reversible.

Both definitions start by “the change is slow enough so that the system is in a sequence of equilibrium states” and this is very confusing. In the literature (most often), “quasistatic” means what I just defined except (sometimes) when the text focuses on explaining what reversibility/irreversibility is and here, writers may use the word quasistatic to mean slow, which in this context means reversible.

Reversible: The change is slow enough so that the system is in a sequence of equilibrium states, in a sense strong enough to ensure entropy never increases at any time because no equilibrium recovery is needed. (I recommend reading a good book of statistical physics to understand why)

Quasistatic: The change is slow enough so that the system is in a sequence of equilibrium states, in the weak sense that the macro-variables are mostly defined (temperature, pressure… are uniform almost everywhere in the system) and that formulas about equilibrium states can be used along the path (such as $dU=TdS-PdV$, $PV=Nk_B T$... ). In this case, equilibrium “catches up” with macroscopic changes but there is still an underlying entropy creation because of equilibrium recovery.

In some cases, you may describe a progressive process as a continuous path in the space of equilibrium states, but it may not necessarily be a true succession of equilibrium states. It is slow enough to draw a continuous path, but it hides a fine-grained disequilibrium. An example is vibrating a piston at supersonic speed to progressively increase the temperature of a gas. This will look like a continuous path of equilibrium states $(V,T)$ but it hides a fine-grained disequilibrium. Another good example is a succession of small free expansions. These transformation are quasistatic but they are not reversible.

For ideal gases, examples are a bit "far fetched" because equilibrium happens very fast and using a piston is a rather "smooth" action. You need violent actions to drive it out of equilibrium. When friction or viscosity is involved, even an (apparently) very slow action is irreversible.

Both definitions start by “the change is slow enough so that the system is in a sequence of equilibrium states” and this is very confusing. In the literature (most often), “quasistatic” means what I just defined except (sometimes) when the text focuses on explaining what reversibility/irreversibility is and here, writers may use the word quasistatic to mean slow, which in this context means reversible.