Does temperature fluctuate? Indirect proof by dynamic glass transition in confined geometries

The Gibbs canonical distribution, dw similar to exp(-E(p, q)/k(B)T)dpdq, seems one of the most solid pillars of statistical physics. Thermodynamics is believed to be a derivative of this distribution. Since the temperature T is introduced, defacto, from a heat bath by the zeroth law of thermodynamics, this distribution cannot represent a genuine temperature fluctuation; all fluctuations are derived from energy fluctuations (delta E). Increasingly, nanoscale problems are attacked by physics (e.g. glass transition), physical chemistry (e.g. nucleation), or biology (e.g. protein folding). The fluctuations are relatively large because the nano-subsystems are small. The fluctuations should, therefore, completely be collected. The von Laue approach [1-3] to subsystem thermodynamics via minimal work for generation of fluctuations also allows the temperature to fluctuate (delta T). For this alternative, statistical physics is a derivative of thermodynamics. Here we show that a decision between the alternatives is possible by a calorimetric determination of the characteristic length of dynamic glass transition in confined geometries.