Exact time-averaged thermal conductance for small systems: comparison between direct calculation and Green-Kubo formalism

Obtaining efficient thermal engines from interacting Brownian particles under time-periodic drivings

We introduce an alternative route for obtaining reliable cyclic engines, based on two interacting Brownian particles under time-periodic drivings which can be used as a work-to-work converter or a heat engine. Exact expressions for the thermodynamic fluxes, such as power and heat, are obtained using the framework of stochastic thermodynamic. We then use these exact expression to optimize the driving protocols with respect to output forces, their phase difference. For the work-to-work engine, they are solely expressed in terms of Onsager coefficients and their derivatives, whereas nonlinear effects start to play a role since the particles are at different temperatures. Our results suggest that stronger coupling generally leads to better performance, but careful design is needed to optimize the external forces.

Particle-shape-, temperature-, and concentration-dependent thermal conductivity and viscosity of nanofluids

In this study, using the Green-Kubo-method-based molecular dynamics simulations, correlations for predicting the thermophysical properties of nanofluids are developed based on particle shape, fluid temperature, and volume concentration. Silver nanofluids with various nanoparticle shapes including spheres, cubes, cylinders, and rectangular prisms are investigated. The numerical study is conducted within the concentration range 0.14-1.4 vol % and temperature range 280-335 K. The relative thermal conductivity and relative viscosity predicated by the proposed correlations are within a mean deviation of 2% and 5%, respectively, as compared with the experimental results from this study and the available literature. The proposed correlation will be a useful tool for engineers in designing the nanofluids for different applications in industry.

Quantum Fokker-Planck-Kramers equation and entropy production

We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.

Thermostatistics of small nonlinear systems: Gaussian thermal bath

We discuss the statistical properties of small mechanothermodynamic systems (one- and two-particle cases) subject to nonlinear coupling and in contact with standard Gaussian reservoirs. We use a method that applies averages in the Laplace-Fourier space, which relates to a generalization of the final-value theorem. The key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator, traditionally required in alternative methods like path integral calculations, which is hardly obtainable in the majority of the cases. For one-particle equilibrium systems we are able to compute the instantaneous (equilibrium) probability density functions of injected and dissipated power as well as the respective large deviation functions. Our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long-term statistics, which preserve the exact same values as computed for linear cases. Actually, we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium, since it affects the average total energy of the system. For the two-particle system we consider each element in contact with a heat reservoir, at different temperatures, and focus on the problem of heat flux between them. Contrarily to the one-particle case, in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system. An important consequence of that it is the temperature dependence of the conductance, which is unobserved in linear(harmonic) models. Our results are complemented by fluctuation relations for the injected power (equilibrium case) and heat flux (nonequilibrium case).

Role of the nature of noise in the thermal conductance of mechanical systems

Focusing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the Lévy-Itô nature of the noise in the thermal conductance. For white noises, we prove that the Lévy-Itô composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a nonequilibrium linearly coupled chain, which signals the independence of mechanical and thermodynamical properties. In contrast, for the nonlinearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.

Time autocorrelation function and Green-Kubo formula: study on a disordered harmonic chain

We have considered heat conduction in a one-dimensional mass-disordered harmonic chain of N particles connected to two Langevin type reservoirs at different temperatures. An exact expression for the boundary heat current-current autocorrelation function in the nonequilibrium steady state (NESS) is obtained in terms of nonequilibrium phonon Green's functions. The time integral of the correlation function gives expected result, both in nonequilibrium as well as equilibrium cases. Using the form of this correlation function we show that asymptotic system size dependence of current fluctuation in NESS for a mass-disordered harmonic chain is N(-α) for different boundary conditions. For free and fixed boundary conditions we get α=1/2 and 3/2, respectively, while for pinned case the fluctuation decays exponentially with system size.

Exact nonequilibrium work generating function for a small classical system

We obtain the exact nonequilibrium work generating function (NEWGF) for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite-time interval. The Jarzynski equality, obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.