Investigation on Energetic Optimization Problems of Stochastic Thermodynamics with Iterative Dynamic Programming

The energetic optimization problem,e.g.,searching for the optimal switching protocol of certain system parameters to minimize the input work,has been extensively studied by stochastic thermodynamics.In this work,we study this problem numerically using iterative dynamic programming.The model systems under investigation are toy actuators consisting of spring-linked beads with loading force imposed on both ending beads.For the simplest case,i.e.,a one-spring actuator driven by tuning the stiffness of the spring,we compare the optimal control protocol of the stiffness for both the overdamped and the underdamped situations,and discuss how inertial effects alter the irreversibility of the driven process and thus modify the optimal protocol.Then,we study the systems with multiple degrees of freedom by constructing oligomer actuators,in which the harmonic interaction between the two ending beads is tuned externally.With the same rated output work,actuators of different constructions demand different minimal input work,reflecting the influence of the internal degrees of freedom on the performance of the actuators.

Nonequilibrium thermodynamics in cavity optomechanics

Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium.As an emerging field,nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes,particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations.Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability,excellent mechanical performance,and ability to operate deep in the quantum regime.Here,we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems.The experimental results in entropy production assessment,fluctuation theorems,heat transfer,and heat engines are highlighted.

A critical transition rule for broadening exponent of fluctuation and its effect on dissipation in chemical reaction-heat conduction coupling systems

A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxes boundary conditions is proposed in this paper. Based on this model,we extend the theory of the broadening exponent of critical fluctuations to cover the chemical reaction-heat conduction coupling systems as an asymptotic property of the corresponding Markovian master equation (ME),and establish a valid stochastic thermodynamics for such systems. As an illustration,the non-isothermal and inhomogeneous Schl-gl model is explicitly studied. Through an order analysis of the contributions from both the drift and diffusion to the evolution of the probability distribution in the corresponding Fokker-Planck equation(FPE) in the approach to bifurcation,we have identified the critical transition rule for the broadening exponent of the fluctuations due to the coupling between chemical reaction and heat conduction. It turns out that the dissipation induced by the critical fluctuations reaches a deterministic level,leading to a thermodynamic effect on the nonequilibrium physico-chemical processes.

On a tilted Liouville-master equation of open quantum systems

A tilted Liouville-master equation in Hilbert space is presented for Markovian open quantum systems.We demonstrate that it is the unraveling of the tilted quantum master equation.The latter is widely used in the analysis and calculations of stochastic thermodynamic quantities in quantum stochastic thermodynamics.