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How do we know that the idea of Entropy is True?

What I mean is, Do we really know "Scientifically" that Entropy of Universe is Bound to increase? Or We know it "Statistically" that Entropy of Universe "Increases"?

Do we know it "Inductively", from the past experiences and our understanding of the universe till now, that Entropy of the universe tends to increase?

Or

There is some "Deductive" proof that the Entropy of the Universe is bound to "Increase"?

In summary, the question is, the idea of Entropy is assumed to be true, Scientifically or Statistically?

I would be very happy if somebody can also provide me some resources which throw light on the history of the development of idea of Entropy.

PS: I do not say that "Statistics" is non-science, just considering the difference of ways of working in two disciplines - "Science" and "Statistics".

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    $\begingroup$ Are you asking about the idea of entropy in general, or its applicability to the entire Universe specifically? $\endgroup$
    – D. Halsey
    Commented Dec 5, 2019 at 17:35
  • $\begingroup$ All scientific knowledge is statistical knowledge. $\endgroup$
    – d_b
    Commented Dec 5, 2019 at 17:45
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    $\begingroup$ @d_b Wait... are you telling me I've been wasting my time taking measurements from my Ultimate Truth Generator $^{TM}$? /s $\endgroup$
    – JMac
    Commented Dec 5, 2019 at 17:55
  • $\begingroup$ ok, entropy can never decrease in an isolated system; in what sense is the universe an "isolated" system having finite entropy (so decrease/increase can be meaningful)? $\endgroup$
    – hyportnex
    Commented Dec 5, 2019 at 19:57
  • $\begingroup$ yes both inductive and deductive reasons, with some assumptions, because there are laws that result in entropy fluctuating, see Wolphram work on cellular automata $\endgroup$
    – user65081
    Commented Dec 6, 2019 at 4:08

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Please read my answers here where I explain what a physics theory is.

There exists a thermodynamics theory, which has the axiomatic laws given here. Uning these laws a plethora of mathematical relations and definitions for simplicity can be defined, and rigorously proven. Thermodynamics is used extensively and its predictions continually validated. The increase in entropy of isolated systems can be shown using these laws and mathematics.

Therefore the entropy of an isolated system either increases or, in the limit, remains constant

It is shown inductively using the laws and the mathematics of the theory of Thermodynamics.

In summary, the question is, the idea of Entropy is assumed to be true, Scientifically or Statistically?

Entropy is a mathematical definition using the variables of the theory of Thermodynamics, and is directly derivable form its laws. It is true mathematically, since the theory is considered valid, laws and all. Within its region of validity, Thermodynamics has not been falsified.

To answer the title question:

How do we know that the idea of entropy is true?

In physics one uses concepts in models and as long as the models are validated, the concepts are considered valid. Truth is an attribute that can given to mathematical theorems. Assumptions about natural observables can either be validated or falsified. At the moment thermodynamics is validated by an enormous amount of data. Observations not validating thermodynamics are mostly in the small dimensions and in the framework of quantum mechanics in general ( like superfluidity). This reduces the phase space of variables where thermodynamics is a valid description of nature. So the concept of entropy is valid in the realm of the phase space of variables where the laws of thermodynamics are valid.

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  • $\begingroup$ Stretche thermodynamics to the universe might though be a bit of an overstretch, since calling an expanding universe as isolated might not be valid. $\endgroup$
    – lalala
    Commented Dec 5, 2019 at 20:56
  • $\begingroup$ It is shown inductively using the laws and the mathematics of the theory of Thermodynamics. This doesn't address the question, which is in any case a duplicate. $\endgroup$
    – user4552
    Commented Dec 5, 2019 at 22:16

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