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Suppose I have a system in my mind which consists of two elementary particles interacting with each other via fundamental interactions. We know that fundamental interactions have $T$-symmetry and there is no arrow of time.

Now, Suppose I add another particle to the system, then another, then another. At what instant, The time-reversal symmetry will break down?

As we know that macroscopic bodies do have an arrow of time. Is there any sharp boundary or what's the parameter that defines, How much sharp the arrow of time is? As I asked this question lately, but not seems to get any useful answer, Everyone just explaining the second law for macroscopic objects.

Young Kindaichi
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  • Time reversal symmetry never breaks down if the underlying particle interactions are T-symmetry invariant. Are you asking about the thermodynamic irreversibility? Such irreversibility arises due to many more microstates being classified as a given macrostate than others (many more 'mixed' configurations than 'unmixed' ones). Otherwise, everything is time-reversal symmetric. – QuantumDot Jul 08 '21 at 18:19
  • I doubt you will get anything that isn't completely qualitative.

    It's similar to asking if we can use QFT to simulate biology. The miscoscopic computations are far too intractable to discover some phase transition from microscopic -> macroscopic physics.

     – user18764 Jul 08 '21 at 18:20
  • @QuantumDot If the system has many more microstates and we start with some arbitrary state, It seems like system is settling into a macrostate with larges microstate. In this sense, there is arrow of time. Do you think given a long time, a symmetric behavior will appear? So that one go back to it's initial configuration. – Young Kindaichi Jul 09 '21 at 07:47
  • Sure. See Poincare Recurrence. – QuantumDot Jul 11 '21 at 20:07
  • then How you will save a second of thermodynamics? – Young Kindaichi Jul 12 '21 at 02:48

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