## What is difference between distinguishable and indistinguishable particles?

If they are distinguishable (Like a helium-3 atom and a helium-4 atom), then you can switch their positions and the system changes. If they are indistinguishable (Like two protons), switching the two particles’ positions makes no physical change because we do not know whether particles switched at all.

### What is distinguishable particles and indistinguishable particles?

Two particles are said to be identical if all their intrinsic properties (mass, spin, charge, etc.) are exactly the same: no experiment can distinguish one from the other. When the two particles are still far away from each other, they are distinguishable due to their spatial separation: we can label them “1” and “2”.

#### Why are quantum particles indistinguishable?

In analogy, if we define particle states in QM by means of partial tracing from the (anti) symmetrized state of the total system, the result is that all 1-particle states are the same, so that all particles (h- particles) are indistinguishable.

**What does it mean when entropy is negative?**

Entropy is the amount of disorder in a system. Negative entropy means that something is becoming less disordered. In order for something to become less disordered, energy must be used. This will not occur spontaneously.

**What is the probability for finding the particles in the same state if they are bosons?**

For bosons, we computed a total of 55 system states, of which 10 have both particles in the same particle state, therefore the probability of finding both particles in the same single particle state is 10/55.

## What is indistinguishability of particles and its consequences?

According to the principle of the indistinguishability of identical particles, if identical particles in a given system of particles are interchanged, the resulting states of the system cannot be distinguished in any experiment and must be regarded as the same physical state.

### Why can entropy not be negative?

In terms of entropy in its absolute value (calculated through the previous equation), no, negative entropy does not exist. A system either has no disorder (which results in a 0 value for S), or some disorder (which results in a positive value for S).

#### How do you know if Delta S is positive or negative?

We say that ‘if entropy has increased, Delta S is positive’ and ‘if the entropy has decreased, Delta S is negative.

**Why does Gibbs paradox arise?**

Gibbs’ Paradox arises when the two gases are identical. If you have two identical gases at the same temperature and pressure in the two compartments, nothing changes when the partition is removed – so there should be no change in the entropy.

**Does Gibbs paradox exist?**

There are in fact two distinct paradoxes that go under the heading of the Gibbs paradox. The original one was formulated by Josiah Willard Gibbs in 1875 [1]. It addresses the mixing of two quantities of ideal gas, and the entropy change that occurs as a result of the mixing process.

## Can two Bose particles exist in the same state?

The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.