Consider the first paragraph of this paper:

A fundamental problem in thermodynamic and statistical physics is to study the response of a system in thermal equilibrium to an outside perturbation. In particular, one is typically interested in calculating the relaxation timescale at which the perturbed system returns to a stationary, equilibrium configuration. Can this relaxation time be made arbitrarily small? That the answer may be negative is suggested by the third-law of thermodynamics, according to which the relaxation time of a perturbed system is expected to go to infinity in the limit of absolute zero of temperature. Finite temperature systems are expected to have faster dynamics and shorter relaxation times—how small can these be made? In this paper we use general results from quantum information theory in order to derive a fundamental bound on the maximal rate at which a perturbed system approaches thermal equilibrium.

Take a system in thermal equilibrium and perturb the system. How long does before the system relaxes back to a stationary, equilibrium configuration?

The excerpt mentions that this relaxation time cannot be made arbitrarily small, because the third-law of thermodynamics stipulates that the relaxation time of a perturbed system is infinite at zero temperature.

The third-law of thermodynamics is stated in the form

The entropy of a perfect crystal at absolute zero is exactly equal to zero.

How can this statement be re-interpreted to mean that the relaxation time of a perturbed system is infinite at zero temperature?


If the entropy goes to zero then the system becomes kinetically trapped in a single microstate (zero entropy) and therefore cannot relax.

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