# Statistical mechanical theory for steady-state systems. III. Heat flow in a Lennard-Jones fluid.

@article{Attard2005StatisticalMT, title={Statistical mechanical theory for steady-state systems. III. Heat flow in a Lennard-Jones fluid.}, author={Phil Attard}, journal={The Journal of chemical physics}, year={2005}, volume={122 24}, pages={ 244105 } }

A statistical mechanical theory for heat flow is developed based upon the second entropy for dynamical transitions between energy moment macrostates. The thermal conductivity, as obtained from a Green-Kubo integral of a time correlation function, is derived as an approximation from these more fundamental theories, and its short-time dependence is explored. A new expression for the thermal conductivity is derived and shown to converge to its asymptotic value faster than the traditional Green…

## 12 Citations

Statistical mechanical theory for steady state systems. IV. Transition probability and simulation algorithm demonstrated for heat flow.

- Physics, EngineeringThe Journal of chemical physics
- 2006

Results obtained for the thermal conductivity and the probability of nonequilibrium work performed on a subsystem of a thermal reservoir along the trajectory in phase space of the subsystem are in good agreement with previous Green-Kubo and nonequ equilibrium molecular dynamics results.

Statistical mechanical theory for non-equilibrium systems. IX. Stochastic molecular dynamics.

- PhysicsThe Journal of chemical physics
- 2009

A stochastic molecular dynamics algorithm is developed for both equilibrium and nonequilibrium systems, which is tested for steady heat flow and for a time-varying, driven Brownian particle.

Theory for non-equilibrium statistical mechanics.

- PhysicsPhysical chemistry chemical physics : PCCP
- 2006

A new theory is reviewed that gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states, and it is shown that this so-called second entropy is maximized in the steady state.

Statistical mechanical theory for steady state systems. VII. Nonlinear theory.

- PhysicsThe Journal of chemical physics
- 2007

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations.

The second entropy: a general theory for non-equilibrium thermodynamics and statistical mechanics

- Physics
- 2009

The second entropy is introduced, which is a new type of entropy that provides a basis for the non-equilibrium thermodynamics of time-dependent systems. Whereas the first or ordinary entropy counts…

Statistical mechanical theory for steady state systems. VI. Variational principles.

- PhysicsThe Journal of chemical physics
- 2006

The approaches of Onsager and Attard are argued to be the only viable theories for nonequilibrium systems and a numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory.

One-Particle Representation of Heat Conduction Described within the Scope of the Second Law

- PhysicsPloS one
- 2016

The Carnot cycle can be viewed as describing a local process of energy-work conversion by a single interacting particle which feature rates of energy transfer and conversion not possible in the classical Carnot development, but that even irreversible local processes might be brought within the scope of this cycle, implying a unified treatment of thermodynamically irreversible and reversible processes.

Equivalence of the EMD- and NEMD-based decomposition of thermal conductivity into microscopic building blocks.

- PhysicsThe Journal of chemical physics
- 2017

The present establishment of the EMD-NEMD correspondence makes the MD analysis of PTCs a robust way to clarify the microscopic origins of thermal conductivity.

Monte Carlo Techniques

- Physics
- 2010

From Washington D.C. to Wall Street to Los Alamos, statistical techniques termed collectively as Monte Carlo (MC) are powerful problem solvers for handling daily tasks.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state.

- Materials ScienceThe Journal of chemical physics
- 2014

A generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear finds that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.

## References

SHOWING 1-10 OF 13 REFERENCES

Statistical mechanical theory for steady state systems. II. Reciprocal relations and the second entropy.

- PhysicsThe Journal of chemical physics
- 2005

The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method, including Green-Kubo formulas for the transport coefficients, as do Langevin dynamics.

The Explicit Density Functional and Its Connection with Entropy Maximization

- Physics
- 2000

The intrinsic Helmholtz free energy, commonly used as a basis for density functional theories, is here given explicitly as a cluster diagram expansion with density field points. Also given are…

Computer Simulation of Liquids

- Economics
- 1988

Introduction Statistical mechanics Molecular dynamics Monte Carlo methods Some tricks of the trade How to analyse the results Advanced simulation techniques Non-equilibrium molecular dynamics…

Theory of simple liquids

- Physics, Chemistry
- 1976

Introduction. Statistical Mechanics and Molecular Distribution Functions. Computer "Experiments" on Liquids. Diagrammatic Expansions. Distribution Function Theories. Perturbation Theories.…

Reciprocal Relations in Irreversible Processes. II.

- Materials Science
- 1931

A general reciprocal relation, applicable to transport processes such as the conduction of heat and electricity, and diffusion, is derived from the assumption of microscopic reversibility. In the…

Thermal conductivity of a shearing fluid.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1993

It is found that the diagonal elements of the thermal-conductivity tensor are independent of the strain rate y up to approximately γ=1.0 and at higher strain rates, the xx and yy elements increase weakly with strain rate while the zz element decreases weakly.

Thermal conductivity of the Lennard-Jones fluid.

- Physics, MedicinePhysical review. A, General physics
- 1986

Statistical mechanical theory for the structure of steady state systems: application to a Lennard-Jones fluid with applied temperature gradient.

- PhysicsThe Journal of chemical physics
- 2004

The constrained entropy and probability distribution are given for the structure that develops in response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory…

͑1993͒. 244105-11 Statistical mechanical theory for steady-state systems

- J. Chem. Phys
- 1058

Phys. Rev. A

- Phys. Rev. A
- 1449