Continuum thermomechanics hinges on the concept of a representative volume element (RVE), which is well defined in two situations only: (i) unit cell in a periodic microstructure, and (ii) statistically representative volume containing a very large (mathematically infinite) set of microscale elements (eg, grains) Response of finite domains of material, however, displays statistical scatter and is dependent on the scale and boundary conditions In order to accomplish stochastic homogenization of material response, scale-dependent hierarchies of bounds are extended to dissipative/irreversible phenomena within the framework of thermomechanics with internal variables In particular, the free-energy function and the dissipation function become stochastic functionals whose scatter tends to decrease to zero as the material volume is increased These functionals are linked to their duals via Legendre transforms either in the spaces of ensemble average velocities or ensemble-average dissipative forces In the limit of infinite volumes (RVE limit (ii) above) all the functionals become deterministic, and classical Legendre transforms of deterministic thermomechanics hold As an application, stochastic continuum damage mechanics of elastic-brittle solids is developed ©2002 ASME

Microstructural Randomness Versus Representative Volume Element in Thermomechanics

Extended Irreversible Thermodynamics: An Overview of Recent Bibliography

Starting out with a survey on different thermodynamical theories concepts of nonclassical thermodynamics such as state space, process, projection, and nonequilibrium contact quantity are discussed. Using the dissipation inequality for discrete systems the existence of a non-negative entropy production is investigated. Internal variables are defined by introducing concepts concerning their properties. Then field formulation of thermodynamics is achieved by use of nonequilibrium contact quantities introduced above. Extended thermodynamics is shortly discussed in comparison with the non-extended one. Material axioms and how to exploit the dissipation inequality are items of the last two chapters.

Fundamentals of Nonequilibrium Thermodynamics

Compound systems consisting of discrete systems being in different contacts with each other are investigated by introducing a limited set of relevant quantum-mechanical observables as a mesoscopic description of discrete systems. The different kinds of partitions between discrete systems are quantum-mechanically characterized. The rate of entropy in closed and work-isolated systems is positive definite, a result which is obtained by identifying parameters of the generalized canonical density operator with the contact temperature of non-equilibrium systems.

Quantum-Thermodynamical Description of Discrete Non-Equilibrium Systems

Abstract Different dynamics of the non-equilibrium canonical density operator, such as Canonical Dynamics, Linear Projection Dynamics, Generalized Robertson Dynamics, and Contact Time Dynamics, especially for time dependent work variables are derived. For two discrete systems in contact the rate of entropy is non-negative, if the contact time is short, and if one of the two discrete systems is in equilibrium and the compound system composed of both is isolated. The contact temperature is identified with one of the Lagrange parameters of the non-equilibrium canonical density operator of the compound system.

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Different Dynamics and Entropy Rates in Quantum-Thermodynamics

Intensive variables of discrete nonequilibrium systems are defined by inequalities which are derivable quantumstatistically for contacts between discrete equilibrium and nonequilibrium systems. These contacts are described by a generalized grand-canonical nonequilibrium density operator of maximal entropy by which heat-, mass-, and power-exchange through the contact can be evaluated. A straightforward calculation yields inequalities whose interpretation enables definitions of intensive nonequilibrium quantities for discrete systems.

Statistical foundation of nonequilibrium contact quantities bridging phenomenological and statistical nonequilibrium-thermodynamics

Excitation energy transfer (EET) and electron transfer (ET) are crucially involved in photosynthetic processes. In reality, the photosynthetic reaction center constitutes an open quantum system of EET and ET, which manifests interplay of pigments, solar light, and phonon baths. So far, theoretical studies have been mainly based on master equation approaches in the Markovian condition. The non-Markovian environmental effect, which may play a crucial role, has not been sufficiently considered. In this work, we propose a mixed dynamic approach to investigate this open system. The influence of phonon bath is treated via the exact dissipaton equation of motion (DEOM), while that of photon bath is via the Lindblad master equation. Specifically, we explore the effect of non-Markovian quantum phonon bath on the coherent transfer dynamics and its manipulation on the current-voltage behavior. Distinguished from the results of the completely Markovian-Lindblad equation and those adopting the classical environment description, the mixed DEOM-Lindblad simulations exhibit transfer coherence up to a few hundred femtoseconds and the related environmental manipulation effect on the current. These non-Markovian quantum coherent effects may be extended to more complex and realistic systems and be helpful in the design of organic photovoltaic devices.

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Coherent excitation energy transfer in model photosynthetic reaction center: Effects of non-Markovian quantum environment.

Correlated driving–and–dissipation equation (CODDE) is an optimized complete second–order quantum dissipation approach, which is originally concerned with the reduced system dynamics only. However, one can actually extract the hybridized bath dynamics from CODDE with the aid of dissipaton–equation–of–motion theory, a statistical quasi-particle quantum dissipation formalism. Treated as an one–dissipaton theory, CODDE is successfully extended to deal with the Herzberg– Teller vibronic couplings in dipole–ﬁeld interactions. Demonstrations will be carried out on the non-Condon spectroscopies of a model dimer system.

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J. Fang

Papers

Statistical foundation of nonequilibrium contact quantities bridging phenomenological and statistical nonequilibrium-thermodynamics

Coherent excitation energy transfer in model photosynthetic reaction center: Effects of non-Markovian quantum environment.

Correlated driving‐and‐dissipation equation for non‐Condon spectroscopy with the Herzberg–Teller vibronic coupling