The Living Thing / Notebooks :

Thermodynamics

Morsels from physics-write-large.

Thermodynamics of computation

Explain this relative to algorithmic statistics <{filename}algorithmic_statistics.rst>_ again?

Could it be that thermal phenomena, forgetful information processing and adaptive evolution are governed by the same stochastic mechanism?

The answer is —- yes! The key to this rather profound connection resides in a universal property of Markov processes discovered recently in the context of non-equilibrium statistical mechanics, and known as the ‘fluctuation theorem’. Typically stated in terms of ‘dissipated work’ or ‘entropy production’, this result can be seen as an extension of the Second Law of Thermodynamics to small systems, where thermal fluctuations cannot be neglected. But it is actually much more than this: it is the mathematical underpinning of irreversibility itself, be it thermodynamical, evolutionary, or else. To make this point clear, let me start by giving a general formulation of the fluctuation theorem that makes no reference to physics concepts such as ‘heat’ or ‘work’.