Current in a diode circuit without a external voltage source Will there be any current in the given circuit? If current exists then why do they exist and what will be the forward and reverse current and voltage(across the diode)?

 A: I assume, you are asking if there can be asymmetric current noise at equilibrium due to the diode.
If there is no magnetic field in the problem, there should be no current. If a system has time-reversal symmetry, i.e. if flipping of all particles makes the system move backwards in time, one can prove there must be no current at equilibrium.
The argument with time-reversal symmetry usually goes from contradiction. Let us assume the system has a single equilibrium with non zero current. The system at equilibrium doesn't change over time. If flip the velocities of all particles, the system will move in reverse and therefore still will not change over time, in other words the system will still be at equilibrium. But if we flip all velocities, the current is going to flip too! I.e. we got two equilibrium states with opposite currents, which contradicts our initial assumption, i.e. there are either several equilibrium states or the current is zero.
Careful. If magnetic field is present, flipping velocities of all particles does not move the system in reverse (convince yourself by considering a single particle in magnetic field). Such systems can have a persistent non-zero current, which is usually determined by the direction of magnetic field.
