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Is it correct to say, that the Newton's laws (or a Newtonian system) is reversible if the friction isn't considered (the fact that the time is of second order $\frac{d^2x}{dt^2}$) and an isolated thermodynamic system is irreversible due to the second law ($\frac{dS}{dt}\ge 0$)? Can somebody elaborate that, because my teacher seems to disagree.

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    $\begingroup$ "that the Newton's laws... is reversible" and "an isolated thermodynamic system is irreversible" don't make sense: a process can be (ir)reversible; a law or a system cannot. "the fact that the time is of second order" how can be time of second order? what does that mean? $\endgroup$ – AccidentalFourierTransform Jan 14 '16 at 19:13
  • $\begingroup$ Newton's laws are the definition of inertial systems, the definition of force and the expression of momentum conservation for contact forces. They say absolutely nothing about energy conservation and one can treat non-conservative forces just fine with them. Obviously they can't say anything about heat, to begin with. Heat is not defined in Newtonian mechanics. $\endgroup$ – CuriousOne Jan 14 '16 at 19:21
  • $\begingroup$ What I try to say, is that it makes equally sense if a ball rolls down of tray or up (without friction) in a newtonian system. The "proces" is then reversible. In thermodynamics a proces will only go one way in a given situation therefore irreversible. $\endgroup$ – Hamid Mohammad Jan 14 '16 at 19:27
  • $\begingroup$ The problem does not even go away with quantum statistics: Under "unitary evolution" (that is under the action of the von Neumann equation) even an isolated quantum system/ensemble (described by a density matrix $\rho$) will not change its entropy. To get entropy changes you always need either some non-unitary evolution ("collapse") or consider an open system with an environment. As soon as you disregard the states of the environment the entropy grows in the considered subsystem due to decoherence effects. $\endgroup$ – Sebastian Riese Jan 14 '16 at 21:38
  • $\begingroup$ Certain kinds of mechanical processes are reversible, even if they occur spontaneously in an isolated system (and are not quasi-static). Two examples of such processes are (a) interconversion of potential energy and kinetic energy without friction and (b) spring-mass systems exhibiting simple harmonic motion. Such processes do not involve dry friction or viscous dissipation of mechanical energy (sometimes called wet viscous friction), both of which generate entropy. $\endgroup$ – Chet Miller Jun 25 '18 at 2:53
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You have to be a bit careful about what you mean when you ask about Newtonian mechanics being reversible or not. As stated in one of the comments newtons mechanics is only a set of rules that tell you how objects accelerate if they are subject to some sets of forces. It does not necessarily tell you the nature of these forces of where they come from.

To understand what processes are reversible i.e. can backtrack their own path let's consider some examples.

Gravity: Here there forces only depend on the distance between two particles, and so does not care about the direction of motion of a particle. The equations of motion are therefore time-revesal symmetric (changing the time direction means changing the direction of all velocities) and any gravitational process is thus reversible.

Friction: Friction mostly depends on the velocity of the object that the friction acts upon. As such these forces are not time-reversal symmetric and fiction processes are not reversible. From a statistical mechanics point of view this is explained by energy dissipating from the system in a non-reveible manner.

Magnetism: Magnetic forces (the Lorenz force) are not time-reversal symmetric either, as is depends on the speed of a particle. Here a funny thing happens under time reversal though. If a particle is moving in a constant magnetic field (tracing out a circle), a you reverse the direction of motion, it will still move on a circle of the same size, but this new circle will only be touch the old circle in a single point.

I have now elaborated a bit. Hope it helped.

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What I try to say, is that it makes equally sense if a ball rolls down of tray or up (without friction) in a newtonian system. The "proces" is then reversible. In thermodynamics a proces will only go one way in a given situation therefore irreversible. – Hamid Mohammad 18 hours ago

When you think of a ball rolling up or down a hill it is easy to imagine that you do not have any friction. "In thermodinamics a process" is often irreversible due to the fact that some part of the energy in dissipated in heat due to what microscopically are frictions phenomena between molecules. So your question is not strickly fair

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Newton's 2nd law and the 2nd Law of Thermodynamics are not mutually exclusive. Certain kinds of mechanical processes are reversible, even if they occur spontaneously in an isolated system (and are not quasi-static). Two examples of such processes are (a) interconversion of potential energy and kinetic energy without friction and (b) spring-mass systems exhibiting simple harmonic motion. Such processes do not involve dry friction or viscous dissipation of mechanical energy (sometimes called wet viscous friction), both of which generate entropy.

So what are the general characteristics of mechanically reversible processes and of irreversible processes, both of which are consistent with the Newton's 2nd law and the 2nd law of thermodynamics?

Mechanically reversible processes involve only conservative forces (such as gravitational body forces) and purely elastic deformational forces (such as springs or more complicated elastic solids), and interconversion of potential energy, elastic energy, and kinetic energy. But there is no kinetic friction and no viscous damping. In mechanically reversible processes, there is no entropy generation within the system during the process and no increase in entropy of the system as a result of the process.

Irreversible mechanical processes are always identifiable as those involving kinetic friction or viscous damping: systems including an actual damper, systems involving very rapid deformation of gases (thus involving viscous gas behavior), liquid systems involving deformation of viscous fluids, systems involving air resistance. All these processes result in generation of entropy within the system, and, in an isolated system, thus result in an increase in entropy of the system.

In addition to irreversibility related to frictional/viscous mechanical behavior, there can also be irreversibility related to heat transfer. This occurs when there are finite (as opposed to infinitesimal) temperature gradients within the system during the process. This also results in entropy generation during the process and an increase in entropy of an isolated system.

Of course there can also be both kinds of irreversibility present in a system during a process.

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