MP, Nonequilibrium thermodynamics as a gauge theory,
Eur. Phys. Lett. 97, 30003 (2012), arXiv:1110.0608
Thermodynamics is the science of irreversible processes. Cycles are a major concept characterizing nonequilibrium behaviour: As a cyclic transformation is completed within a system, some physical quantity (energy, matter, etc.) is transferred across the environment from a reservoir to another in a way that degrades its “quality”, resulting in the production of entropy. From a probabilistic point of view, entropy production quantifies the probability that a cycle is run in one way rather than its opposite, characterizing the arrow of time. Another field of physics where cycles (or loops) play a major role is Quantum Field Theory, where the so-called Wilson loops of certain “gauge fields” are the crucial invariant observables. Importantly, a gauge field emerges from the requirement that the theory enjoys a local symmetry. Indeed, this is more than an analogy: in this paper I cast thermodynamics in the same language as the Quantum Field Theory of gauge fields. One important question to be answered is: What is the local symmetry underlying thermodynamics? I show that this symmetry is purely probabilistic, and it involves transformations of prior probability that an observer retains about a system. That is, in a way, I prove that also in thermodynamics the observer’s personal opinion shouldn’t influence the validity of a physical law.