## Thursday, November 10, 2016

### Irreversibility is an emergent property

Time has a direction. Macroscopic processes are irreversible. Mixing is a simple example. The second law of thermodynamics encodes universal property of nature.
Yet the microscopic laws of nature [Newton's equations or Schrodinger's equation] are time reversal invariant. There is no arrow of time in these equations. So, where does macroscopic irreversibility come from?

It is helpful to think of irreversibility [broken time-reversal symmetry] as an emergent property. It only exists in the thermodynamic limit. Strictly speaking for a finite number of particles there is a "recurrence time" [whereby the system can return to close to its initial state]. However, for even as few as a thousand particles this becomes much longer than any experimental time scale.
There is a nice analogy to spontaneously broken symmetry in phase transitions.  Strictly speaking for a finite number of particles there is no broken symmetry as the system can tunnel backwards and forwards between different states. However, in reality for even a small macroscopic system the time scale for this is ridiculously long.

Deriving irreversibility from microscopic equations is a major theoretical challenge. The first substantial contribution was that of Boltzmann's H-theorem. There are many subtleties associated with why it is not the final answer, but my understanding is superficial...

This post was stimulated by some questions from students when I recently visited Vidyasagar University.

#### 1 comment:

1. About reversibility. You say that "even at a thousand atoms..." Its nowhere near that for single, isolated molecules. "Significant" recurrences never occur even at 7 atoms, at modest energies.
If you excite a C-H stretch in for example acetaldehyde the energy will move out in a about 100 psec, never to return (never ever because the energy will radiate away). You only need a few, say 10, coupled quantum states to see this! Its a pity that physicists almost never look at isolated, gas phase, molecules because they are such a rich set of similar systems.