&gt; Our direction of time is defined by the observation that entropy (or &quot;chaoticness&quot;) always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible.<p>Entropy does not always increase in time, because entropy is rarely a function of time. The most common meaning of the word is a thermodynamic quantity that is not, in general, defined in non-equilibrium states. It is a function of state variables rather than time.<p>What people are talking about when they say &quot;entropy increases in time&quot; is actually some variant of minus Boltzmann H-function. This kind of resembles thermodynamic entropy, but is a distinct and less general concept. There are processes where entropy gets higher but &quot;entropy&quot; (minus Boltzmann H-function) get lower.<p>If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. It is not even clear how to define entropy of the system in between, since it is in highly non-equilibrium state.