## 12 Citations

### Links between microscopic and macroscopic fluid mechanics

- Physics
- 2003

The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories…

### Liouville's theorems, Gibbs' entropy, and multifractal distributions for nonequilibrium steady states

- Physics
- 1998

Liouville’s best-known theorem, ḟ({q,p},t)=0, describes the incompressible flow of phase-space probability density, f({q,p},t). This incompressible-flow theorem follows directly from Hamilton’s…

### Noise-driven numerical irreversibility in molecular dynamics technique

- PhysicsComput. Phys. Commun.
- 2005

### Energy conservation in molecular dynamics simulations of classical systems.

- PhysicsThe Journal of chemical physics
- 2012

Simulations show that inclusion of the first non-trivial term in this expansion of the time step length reduces the standard deviation of the energy fluctuations by a factor of 100 and analytically and numerically shows that energy conservation is not sensitive to round-off errors.

### Nosé–Hoover nonequilibrium dynamics and statistical mechanics

- Physics
- 2007

At equilibrium Nosé's 1984 revolutionary thermostat idea linked Newton's mechanics with Gibbs' statistical mechanics. His work expanded the scope of isothermal and isobaric simulations. Nosé–Hoover…

### Time-reversal symmetry in dynamical systems: a survey

- Physics, Mathematics
- 1998

### D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations

- MathematicsSymmetry
- 2020

The conditions of the symmetric property of the unique solution of symmetric functional differential equations, an illustration of a particular symmetric equation, are shown.

## 42 References

### Resolution of Loschmidt's paradox: The origin of irreversible behavior in reversible atomistic dynamics.

- PhysicsPhysical review letters
- 1987

Nosromane-bar mechanics provides a link between computer simulations of nonequilibrium processes and real-world experiments and shows that irreversible behavior consistent with the second law of thermodynamics arises from completely reversible microscopic motion.

### Stationary nonequilibrium ensembles for thermostated systems.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

The Kawasaki distribution function formalism, which is based on the Liouville equation, is shown to give a good description of the transient and the stationary behavior of proposed measures for chaotic dynamical systems, with particular reference to thermostated nonequilibrium systems.

### Dissipative Irreversibility from Nosé's Reversible Mechanics

- Physics
- 1987

Abstract Nose's Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic…

### The concept of irreversibility in the kinetic theory of gases

- Physics
- 1987

Abstract We present here a discussion of the concepts of “reversibility” and “irreversibility” of an evolution. In section 1, several reversibility concepts and the notion of an H-functional are…

### Time-reversible continuum mechanics

- Physics
- 1994

Levesque and Verlet developed a time-reversible and “bit-reversible” computational leapfrog algorithm. Their algorithm uses integer arithmetic and is exactly time reversible to the last computational…

### Hamiltonian formulation of the Gaussian isokinetic thermostat.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

The usual ~Lagrangian and Hamiltonian! descriptions of classical mechanics are formulated in terms of variational principles, which allow a compact representation of the system by a single function, simplify perturbation theory, and make a connection with quantum mechanics.

### Molecular dynamics and time reversibility

- Physics
- 1993

We present a time-symmetrical integer arithmetic algorithm for numerical (molecular dynamics) simulations of classical fluids. This algorithm is used to illustrate, through concrete examples, that…

### Time-reversible dissipative attractors in three and four phase-space dimensions

- Mathematics
- 1997

We establish the dissipative nature of several three- and four-dimensional time-reversible phase-space flows and study their ergodicity. Three- and four-dimensional generalizations of the equilibrium…