What's the differences between time in Physics and time in everyday use? OK. This question might sound as not a good question, but the word 'time' is so confusing to me. I mean thermodynamics says time is the product of entropy. Relativity says time is relative. Quantum Mechanics says time doesn't exist, and that we can derive any given equation without involving time like Kepler's law. And I thought time measurement such as hour or second is just what we invented for conveniences on daily lives. 
So are definition of time in Physics difference from time we associated in everyday life?
 A: In layman use, across the world (ignoring time zones), someone who is walking observes the same time as you. In physics, however, that person has his/her own time, relative to that person. In classical thermodynamics, time is the same as layperson's time. It is just described in a different way. Quantum mechanics doesn't say that time doesn't exist.
A: The oldest perspective is the philosophical one established by Aristote; modified by Mach and then Barbour


*

*Time is an aspect of change (ie motion) 


There is the mathematical perspective


*Time when mathematically conceived is just a parameter in the equation. 


This in fact has nothing to do with time - it's purely formal 
Physically there are a couple of candidates for the arrow of time


*The direction of increasing entropy 

*The direction in which the universe is expanding
A: In everyday (or casual) use "time" is often (mis-)taken to mean


*

*duration, or

*a coordinate assignment to indications or entire events ("coordinate time").
In contrast, the current, correct and careful meaning of "time" in Physics is based on Einstein's definition of "time" as "the position of the little hand of my watch"; i.e. generally as any one particular indication of any particular participant; or (also) as the entire ordered set of indications of any particular participant.
A: Here are the three primary definitions of time in 3 prominent English language dictionaries:

American Heritage Dictionary 
  also thefreedictionary.com 
  1a. A nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future.
  1b. An interval separating two points on this continuum; a duration:a long time since the last war; passed the time reading.
  1c. A number, as of years, days, or minutes, representing such an interval:ran the course in a time just under four minutes.
  1d. A similar number representing a specific point on this continuum, reckoned in hours and minutes:checked her watch and recorded the time, 6:17 AM.
  1e. A system by which such intervals are measured or such numbers are reckoned:solar time.
Merriam-Webster Dictionary (also the same as in the Random House dictionary)
  1a. the measured or measurable period during which an action, process, or condition exists or continues : duration 
  1b. a nonspatial continuum that is measured in terms of events which succeed one another from past through present to future
Oxford English Dictionary (from  Compact OED © 1971)
  1. A limited stretch or space of continued existence, as the interval between two successive events or acts, or the period through which an action, condition, or state continues.  

This is being used, by me, as an authoritative source so that this is simply no one's particular POV.  Being that these are general dictionaries, the only POV that you can accuse these definitions as having is the "English language" POV.  AH and OED live on opposite sides of the pond and MW is an old standard.
Now there are two grosser POVs to represent, and of one of these POVs, there are two sub-POVs to consider:
Time as phenomenon or concept like space or spacetime or cosmos or life or consciousness or God or some other "big idea" like that.
Time as a quantity of measurement like length or mass or electric charge or temperature or some "operational definition" like that.
Of the operational or measurement POV, there is another split.  Measurement with regard to physical systems (more objective) and measurement with respect to experience of a human or some other conscious being (more subjective, time being something we "feel").  The reason that these are two sides of the same coin is that all clocks or rulers or voltmeters are really just extensions of our senses or our experiential measurement of these quantities.  We gauge how big a bug is or another person or a building or a mountain, with respect to how big it appears alongside us.  We have an experiential measure of this quantity called size without a meter stick.  Similarly we have an experiential measure of time without external clocks.  But both our experience of this measurement or our usage of a measuring device (a clock) is acting on the same quantity.  It's just that our bare-handed biological, experiential measure might not be as tight as the one using a 133Cs clock.
Time as phenomenon is a perspective that is both differentiated from the Time as measurement perspective and solidly supported by the English language dictionaries.  Leaving it out of the lede is not NPOV.  In addition, it is more fundamental.  During the first million years of the existence of the Universe there were certainly no sentient beings around to be experiencing or measuring time, but time existed.  There were physical processes going on that had quantitative relationships with each other and with time.  There was an $x(t)$  and there was a $t$, and no one was around measuring it.  Let's not get into any stupid Tree-falling-in-the-forest-with-no-one-around-to-hear-it,-does-it-make-a-sound? baloney.  Of course it did.  Time has been around a lot earlier than there had been anyone in the Universe measuring anything, including time.
Time is about the existence of things, about us and other things in the Universe.  The OED supports that.  Time is apparently unidirectional as we (and anything that is not an antiparticle ) commonly experiences it.  In addition, it's single-dimensional (unlike space) so, the common understanding of time is that time progresses in one direction.    One event happens after another in an ordered sequence that can be placed on the real number line.  Just like "greater than" > and "less than" < have meaning with real numbers, "earlier" or "previous"  and "later" or "subsequent" have comparable meaning with respect to time.
So, in two sentences, all three major POVs are comprehensively (not exhaustively) introduced.  We have Time as phenomenon, the fundamental definition, first with "past", "present" and "future".  This can be footnoted for a cutey and simple definition from John Wheeler: "Time is what prevents everything from happening at once." (along with "Space is what prevents everything from happening to me.")  Then we have Time as measurement or the "operational definition", both regarding the physical systems and regarding the human (or sentient) experience (we can measure the duration of something or we can guess how long it was from our experiencing it).  And we can footnote that with the statement from Einstein that "Time is what clocks measure."  Although not as comprehensive, both cited statements express, in a nutshell, what ''time'' is thought of fundamentally and what ''time'' is as a measurement.  They're good.
Also, rate of change of a quantity is directly related to and a consequence of time.  It is simply the reciprocal of time, $\frac{1}{t}$, or frequency.  It belongs in the measurement sentence.  It is often how time is measured or experienced. 
The more fundamental POV of time is that of Wheeler and the more operational POV is that of Einstein.  We can get the key concepts down with two concise sentences:

Time is the indefinite continued progression of existence and events that occur in apparently irreversible succession from the past through the present to the future.  Time is a component quantity of various measurements used to sequence events, to compare the durations of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience.

