Fourier Heat Conduction as a phenomenon described within the scope of the Second Law

The historical development of the Carnot cycle necessitated the construction of isothermal and adiabatic pathways within the cycle that were also mechanically "reversible" which lead eventually to the Kelvin-Clausius development of the entropy function where the heat absorption is for the diathermal (isothermal) paths of the cycle only. It is deduced from traditional arguments that Fourier heat conduction involves mechanically "reversible" heat transfer with irreversible entropy increase. Here we model heat conduction as a thermodynamically reversible but mechanically irreversible process. The MD simulations conducted shows excellent agreement with the theory. Such views and results as these, if developed to a successful conclusion could imply that the Carnot cycle be viewed as describing a local process of energy-work conversion and that irreversible local processes might be brought within the scope of this cycle, implying a unified treatment of thermodynamically (i) irreversible, (ii) reversible, (iii) isothermal and (iv) adiabatic processes.Comment: 10 pages, 2 figures. Material for talk at conference and ICNPAA 2014 (Narvik, Norway) Conference Proceeding

A reversible infinite HMM using normalised random measures

We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Markov chain. The resulting prior over infinite transition matrices is closely related to the hierarchical Dirichlet process but enforces reversibility. A reinforcement scheme has recently been proposed with similar properties, but the de Finetti measure is not well characterised. We take the alternative approach of explicitly constructing the mixing measure, which allows more straightforward and efficient inference at the cost of no longer having a closed form predictive distribution. We use our process to construct a reversible infinite HMM which we apply to two real datasets, one from epigenomics and one ion channel recording.Comment: 9 pages, 6 figure