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(Inspired from this question (A) which unfortunately the link in the selected answer is now 404 broken (which might have contained my answer), thus cannot read any deeper than that)

From the above links, and my past understanding, I understood that time has an arrow, which in here Paul Davis made a distinction between the two subtle types

  1. Arrow as an asymmetry: That processes don't behave in an identical way when t is replaced by -t. Many examples including the CP violations, dampened wave equations, or in optics where some signals are engineered in a way so that it behaves differently if t is repalced by -t

  2. The (psychological) daily life experience of the flow of time: Which he and many physicists considered as an illusion, while some others considered as an emergent property of time

I also understood that time is often used as a parameter to track how the states of a system changes

And in the longest answer of this link, it was mentioned how we often use (near) periodic events as clocks to measure time

Since the best answer from (A) mentioned the following

Our scientific time definition uses the concept of entropy to codify change in space, and entropy tells us that there exists an arrow of time.

In a steady state there can be a number of properties unchanged in time (even though the universe as a whole increases entropy steadily due to the 2nd Law of thermodynamics)

Thus this brought the question

If we restrict ourselves to within the steady state and measure some properties (hence the entropy production cannot be measured since it is outside the system, and within the system the net change in entropy is 0 thus not changing with time), are we able to tell how much time has elapsed based on just measuring these properties that are not changing with time?

Or put it in another way, can we still tell time from within the system if entropy in the system remains unchanged?

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If we restrict ourselves to within the steady state and measure some properties

Steady states do not exist in isolation . Any mass/body in isolation in space will radiate black body radiation and its thermodynamic variables will be changing, and thus will not be in a "steady state".

(hence the entropy production cannot be measured since it is outside the system, and within the system the net change in entropy is 0 thus not changing with time),

It is useful to think of entropy in terms of statistical mechanics, as coming from

entropy is a logarithmic measure of the number of states with significant probability of being occupied

In a body in isolation due to the multitude of interactions between molecules and black body radiation entropy will be increasing as the number of microstates increases. Thus one can estimate entropy and measure its increase.

are we able to tell how much time has elapsed based on just measuring these properties that are not changing with time?

For thermodynamic properties not to be changing with time means that energy is being supplied to the system to balance black body radiation. Again in the total system ( energy supplier and system supplied), entropy can be estimated as well as its increase

Or put it in another way, can we still tell time from within the system if entropy in the system remains unchanged?

This is a different question. If entropy is unchanged then time cannot be defined. But to keep entropy unchanged in a subsystem, as I said above, energy has to be supplied, otherwise by black body radiation entropy changes. The entropy of the whole system can be be estimated and provide time.

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  • $\begingroup$ So you mean if the thermodynamic properties that are measured are in the steady state (and if we are not measuring those in the energy supplier) then we won't be able to measure the change in the number of microstates thus cannot define or tell time based on what we measured. So in order to tell the entropy change and hence define time we also need to measure the thermodynamic properties of the energy suppliers and the photons in the black body radiation emitted? $\endgroup$ – Secret Mar 1 '15 at 7:07
  • $\begingroup$ So using the most extreme case of an equlibrium system, the heat death of the universe, then since everything (including the black body radiation) are in equlibrium, nothing is changing thus not only we cannot have an arrow of time as mentioned by some related questions, but we also cannot define time (let alone the flow of time that we commonly experienced) at all? $\endgroup$ – Secret Mar 1 '15 at 7:12
  • $\begingroup$ You need a model for the heat death of the universe, which with general relativity etc is not a simple matter. It is simpler to think of a chunk of matter in the void. Its entropy will be increasing by counting the bb photons leaving it. In the end the chunk will be at 0 temperature will have as a limit 0 entropy, and all the entropy will be in the wave of black body photons receding to infinity. When the last photon leaves time will stop for the chunk $\endgroup$ – anna v Mar 1 '15 at 7:21
  • $\begingroup$ Just saw that final addenum on the previosu comment, thanks $\endgroup$ – Secret Mar 1 '15 at 7:42

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