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, se ems 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 thermodynamic s, this distribution cannot represent a genuine temperature fluctuation; al l fluctuations are derived from energy fluctuations (delta E). Increasingly , nanoscale problems are attacked by physics (e.g. glass transition), physi cal chemistry (e.g. nucleation), or biology (e.g. protein folding). The flu ctuations are relatively large because the nano-subsystems are small. The f luctuations should, therefore, completely be collected. The von Laue approa ch [1-3] to subsystem thermodynamics via minimal work for generation of flu ctuations also allows the temperature to fluctuate (delta T). For this alte rnative, statistical physics is a derivative of thermodynamics. Here we sho w that a decision between the alternatives is possible by a calorimetric de termination of the characteristic length of dynamic glass transition in con fined geometries.