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In the context of driven diffusive systems, for thermodynamic transformations over a large but finite time window, we derive an expansion of the energy balance. In particular, we characterize the transformations which minimize the energy dissipation and describe the optimal correction to the quasi-static limit. Surprisingly, in the case of transformations between homogeneous equilibrium states of an ideal gas, the optimal transformation is a sequence of inhomogeneous equilibrium states.
We extend certain basic and general concepts of thermodynamics to discrete Markov systems exchanging work and heat with reservoirs. In this framework we show that the celebrated Clausius inequality can be generalized and becomes an equality, signific
We note that the social inequality, represented by the Lorenz function obtained plotting the fraction of wealth possessed by the faction of people (starting from the poorest in an economy), or the plot or function representing the citation numbers ag
By generalizing the traditional concept of heat dQ and work dW to also include their time-dependent irreversible components d_{i}Q and d_{i}W allows us to express them in terms of the instantaneous internal temperature T(t) and pressure P(t), whereas
Quantitative isoperimetric inequalities for anisotropic surface energies are shown where the isoperimetric deficit controls both the Fraenkel asymmetry and a measure of the oscillation of the boundary with respect to the boundary of the corresponding Wulff shape.
To make progress in understanding the issue of memory loss and history dependence in evolving complex systems, we consider the mixing rate that specifies how fast the future states become independent of the initial condition. We propose a simple meas