minimum entropy production
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Abstract We investigate the problem of minimizing the entropy production for a physical process that can be described in terms of a Markov jump dynamics. We show that, without any further constraints, a given time-evolution may be realized at arbitrarily small entropy production, yet at the expense of diverging activity. For a fixed activity, we find that the dynamics that minimizes the entropy production is given in terms of conservative forces. The value of the minimum entropy production is expressed in terms of the graph-distance based Wasserstein distance between the initial and final configuration. This yields a new kind of speed limit relating dissipation, the average number of transitions and the Wasserstein distance. It also allows us to formulate the optimal transport problem on a graph in term of a continuous-time interpolating dynamics, in complete analogy to the continuous space setting. We demonstrate our findings for simple state networks, a time-dependent pump and for spin flips in the Ising model.

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of the quantized conductances in other phenomena of nature, the concept of quantized entropy current can be established and it eases the description of a transferred quantized energy package. This might yield a universal transport behavior of the microscopic world. During the transfer of a single energy quantum, hν, between two neighboring domains, the minimum entropy increment is calculated. It is pointed out that the possible existence of the minimal entropy transfer can be formulated. Moreover, as a new result, it is proved that this minimal entropy transfer principle is equivalent to the Lagrangian description of thermodynamics.

The analysis of sentence lengths in the inaugural speeches of US presidents and the annual speeches of UK party leaders is carried out. Transcripts of the speeches are used, rather than the oral production. It is discovered that the average sentence length in these speeches decreases linearly with time, with the slope of 0.13 ± 0.03 words/year. It is shown that among the analyzed distributions (log-normal, folded and half normal, Weibull, generalized Pareto, Rayleigh) the Weibull is the best distribution for describing sentence length. These two results can be considered a consequence of the principle of least effort. The connection of this principle with the well-known principles of maximum and minimum entropy production is discussed.

The concept of an intelligent control system for a complex nonlinear biomechanical system of an extension cableless robotic unicycle discussed. A thermodynamic approach to study optimal control processes in complex nonlinear dynamic systems applied. The results of stochastic simulation of a fuzzy intelligent control system for various types of external / internal excitations for a dynamic, globally unstable control object - extension cableless robotic unicycle based on Soft Computing (Computational Intelligence Toolkit - SCOptKBTM) technology presented. A new approach to design an intelligent control system based on the principle of the minimum entropy production (minimum of useful resource losses) determination in the movement of the control object and the control system is developed. This determination as a fitness function in the genetic algorithm is used to achieve robust control of a robotic unicycle. An algorithm for entropy production computing and representation of their relationship with the Lyapunov function (a measure of stochastic robust stability) described.