# Can observation change entropy?

I don't know whether this even makes any sense, but if 'observation' can be considered as 'recieving and reading information', can an act of observation (of a system) change (increase or decrease) its entropy?

• Take a closed box filled with oxigen. Open it up to observe it. What happened to the entropy of the box? Feb 9, 2016 at 19:08
• do you want a fundamental example where entropy is not changed ? a little tricky but it does fit the case
– user46925
Feb 9, 2016 at 19:42
• @igael Yes, of course. Feb 10, 2016 at 3:14
• passive observations of the black body radiation are still observations. Let's observe a galaxy at 7 billion ly and assume the worst case where the entropy produced by the observation may change the entropy of a near galaxy, meaning that its effect is not neglectable. In an expanding universe , the device can't send today a signal to the 7 billion ly galaxy and then can't never influence its entropy, In a static universe, the same at any distance lets a delay between a passive observation and a possible change.
– user46925
Feb 10, 2016 at 4:07
• Don't get hung up on the information aspect. It's not essential. The essential property of observations are that they are irreversible, which answers your question in a single word. Yes, observations do change entropy. Feb 10, 2016 at 4:41

There are two notions of "state" in statistical mechanics. A "microstate" contains 100% of all the information about a physical system at a given point in time. A "macrostate" is a probability distribution of microstates. If a macrostate assigns every every microstate $$i$$ has a probability $$p_i$$, the entropy is $$S = -k_B \sum_i p_i \log(p_i)$$. If a macrostate assigns an even probability $$1/\Omega$$ to $$\Omega$$ microstates, we can see the entropy is $$S = k_B\log \Omega$$, which is the more traditional expression.

On a fundamental level there is only one true microstate your system is in at a given moment. Entropy comes from uncertainty over which microstate is the true one.

The point is that different observers might describe reality with different macrostates, For example, say your room is very messy and disorganized. This isn’t a problem for you, because you spend a lot of time in there and know where everything is. Therefore, the macrostate you use to describe your room contains very few microstates and has a small entropy. However, according to your mother who has not studied your room very carefully, the entropy of your room is very large.

So yes, the entropy of a system will decrease upon measurement, assuming your measurement is good and your macrostate becomes better resolved. However, global entropy is, with overwhelming probability, always going to increase anyway, even if the entropy of a subsystem decreases.

Addendum: Introductory discussions of entropy are often abstract and confusing. It can be helpful to look at concrete examples. Many statistical mechanics textbooks literally "count" the number of microstates of a box of gas with $$N$$ particles in a volume $$V$$ with total energy $$U$$. This is given by the Sakur-Tetrode equation. (Perhaps there is a good derivation on the internet somewhere. I like the one in Dan Schroeder's textbook too.) Here the microstates are labelled by all the positions and momenta of all $$N$$ particles, and the number of microstates is given by an integral over the volume of microstates with integration measure

$$\frac{1}{h^{3N}}d^3 x_1 \ldots d^3 x_N d^3 p_1 \ldots d^3 p_N$$ Hopefully that should give you a concrete way to think about entropy.

• Excellent. In general, popularised explanations are simplified to the point of being confused or even self-contradictory and the only way to keep to sense is to keep in contact with the first principles at all times. Whenever an eminent physicist writes about the arrow of time, and starts treating entropy as if it were a thing in itself, you know that it is time to bin the book and discard the physicist. Jun 14, 2019 at 7:01

There are a lot of definitions of entropy. I was just trying to get an answer to the same question. I studied physics and the concept of entropy was horrible as the definition kept changing. The old historical Entropy is not a physical thing; it started as some number that seemed to explain why you could not reverse most processes.

Now in the modern world you can define the Maximum or Equilibrium Entropy by the amount of information you need to describe a process. This Maximum doesn't change. But as I write this message in English I'm not making use of the information capacity; because of that some people will state that the actual entropy is lower. If we have temperature the bits in this message will switch around and we will end with a message you can't describe with less than the maximum information.

If you already have information about the process, the remaining information you need to know is lower. The big question is whether this is a physical property.

In a quantum system where Alice and Bob each have a brain capacity of one and Bob knows a number between 0,1 and Alice knows nothing both have a maximum Entropy of 1. Bobs used entropy is in this case is 1, the used entropy of Alice 0. If Alice asks Bob about his number and remembers it she has also a used entropy of 1. Now with all additional information we know the entropy of [Alice + Bob] is 1 as both contain the same information. The maximum entropy of Alice + Bob is 2.

Nobody ever defined Entropy in a way that allows us to give a clear definition of the Amount of Entropy the system Alice+Bob has is a coupled state and while it might play a role in their physical behavior we don't have a way to measure how much they know from each other.

That makes the term "Entropy" a somewhat confusing term.

By the way; if you believe in Realism in its strict form the answer is NO; your observation can't change a physical property. Or as I concluded when I learned about entropy; NO, according to most descriptions entropy can't be a physical property.

If you abandon realism the actual used entropy could be a physical property. Any physical law which depends on your knowledge would be the end of Realism.

• "That makes the term "Entropy" a completely useless and confusing term." Tell that to Clausius! [Even $I$ thought that the concept of entropy vastly increased the predictive power of thermodynamics!] May 11, 2019 at 22:49
• Yes, it did increase it but it wasn't clear what it was and with that the definition has changed about 20 times in the past 100 years. I don't mean that it is useless to thing about it. It is useless because you don't know what someone means when he says it. The maximum entropy is useful and can be defined. But the "entropy" below maximum has a subjective meaning. Nut I changed it a little :-)
– Daan
May 11, 2019 at 22:59

I’m going to go out on a limb here and “answer” instead of comment because I struggled with the concept of entropy for so long until I came to this simple conceptual definition: entropy is the measure of how far away a system is from equilibrium. From a Physics 101 point of view, observation cannot change this. If a box of gas is at equilibrium, no amount of observation is going to change it to a state less in equilibrium. Your observation might give you perfect information about the microstate the box of gas is in, but that does not make it more likely to transition to a microstate not in equilibrium. Here it is helpful to consider equilibrium in two ways. One is that in equilibrium you cannot extract work from the system. A box of gas in equilibrium cannot be made to move a piston or anything else. Two is to consider that in equilibrium the system is in a macrostate that has many more microstates similar to it (in equilibrium) than any macrostate not in equilibrium. Though the movements of the gas molecules are random, the sheer number of possible equilibrium microstates makes it highly probable that the system will evolve to another equilibrium microstate rather than into a non-equilibrium microstate, of which there are far, far fewer. With information theory there are other considerations, but these are beyond the physics 101 level, so if you’re just starting out and are confused by entropy (like I was) and just want a simple way to think about what it describes, then the above is hopefully helpful.

In my mind, to unravel this question, we need to consider the simplest scenario possible. So, let us disregard quantum systems and small systems and consider only statistical mechanics of big classical systems.

Entropy is defined as the log of the number of microstates at a given energy E (up to the Botlzmann constant). Namely, for a classical Hamiltonian, we have to find all the configurations that correspond to the same desired energy value E. This implies that the only information you have about the system is it's energy and the Hamiltonian governing its equilibrium properties. Now, suppose that you have $$\Omega$$ such allowed microstates. Introducing a measurement, or gaining information about the system, forces you to consider more constraints about your microstates. This can only reduce the number of allowed microstates or leave them unchanged.

I hope it helps.

In unobserved condition, the system has maximum entropy but when an observer is introduced, the entropy will suddenly drop to minimum because of the definite perception of the observer. Then it will gradually increase on subjection to public. :)

• What do you mean by "subjection to public"??? Jun 21, 2017 at 11:20