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In this paper, we develop an energy-based dynamical system model driven by a Markov input process to present a unified framework for stochastic thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic dissipativity, losslessness and accumulativity theory, we develop a nonlinear stochastic port-Hamiltonian system model characterized by energy conservation and entropy non-conservation laws that are consistent with statistical thermodynamic principles. In particular, we show that the difference between the average stored system energy and the average supplied system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration, whereas the difference between average system entropy production and the average system entropy consumption is a submartingale with respect to the system filtration. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'. [ABSTRACT FROM AUTHOR]

In this paper, we develop a covariance control problem to address a tradeoff between H 2 performance and H ∞ disturbance attenuation. In particular, we formulate a mixed-norm H 2 / H ∞ and entropy covariance control problem that guarantees that the state covariance of an uncertain dynamical system driven by white noise is upper bounded in the sense of the cone of nonnegative definite matrices by a given threshold matrix via state feedback as well as output feedback control. This is accomplished by combining H 2 covariance control theory and mixed norm H 2 / H ∞ control theory. By using suitable transformations involving dynamic weighting on the complimentary sensitivity system transfer function, the proposed formulation is applicable to robustness problems involving nominal performance subject to a robust stability requirement. The proposed formulation allows for solutions via semidefinite programming. Finally, two illustrative numerical examples are provided to show the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]