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Based on the idea of that particle decay represents nothing but a kind of thermodynamic process due to its spontaneity, we here explore a n ew kind of heat engine: particle Carnot engine (PCE), which satisfies Carnot’s theorem. The result shows that any single particle carries its quantized intrinsic entropy, and the total entropy never decreases for any decay process. Particle thermodynamic laws analogous to the usual ones are proposed, among which the momentum conservation principle is specially introduced that will determine the irreversibility of particle decay. Moreover, we also develop the operational definitions of particle state functions, including Boltzmann relationship, which can be used to discuss the thermodynamic properties of particle objects. Thus, our study can provide a new theoretical framework to investigate particle physics.

Through generalizing in some interdisciplinary areas [^{ }quantum heat engine (employing as working agents multi-level systems instead of gas-filled cylinders) [

To develop the full analogy between particle object and thermodynamic system, we need to recall that particle decay is exactly representing a kind of spontaneous process, just as heat passing from a higher to a lower temperature (the situation is shown as

with moving velocity

of which the differential reads

here

it yields the transition from independent variables

The differential above suggests that

Now, let us imagine there is a particle

the two heat reservoirs, with, in each cycle (called particle Carnot cycle), heat

(i) Isothermal expansion of

(ii) Emerging of

(iii) Isothermal compression of

field at

(iv) Breaking of thermal contact and continuance of adiabatic compression of

In the way, PCE is made up, and all PCEs operating between the same two reservoirs have the same efficiency of converting bound energy to useful form, that is

Complicated system | Particle object | |
---|---|---|

⇓ | ⇔ | ⇓ |

Angular momentum | ⇔ | Intrinsic spin |

Machinery wave | ⇔ | de Broglie wave |

Thermodynamic behaviors | ⇔ | Thermodynamic exhibition |

here the adiabatic case of

livered, the efficiency of presented PCE should be zero, namely

Moreover, considering no engine more efficient than PCE, we have

This is referred to as Clausius’ inequality, in which, “=” is allowed only for reversible decay process (i.e.

ure 2). Importantly, inequality (7) can lead directly to the principle of increasing entropy for particle physics: in any decay process, the total entropy of relevant particles increases or remains constant, but cannot decrease. In particular, for

the entropy increase trend can be shown as

Thus we say it is the principle that determines the irreversibility of particle decay.

So far, based on the obtained above, we present the following particle thermodynamic laws.

0th law: Particle objects have well-defined values of some set of state variables, being of two types: to some extensive variables (such as

1st law: Energy is conserved for all particle processes. The law claims that the particle perpetual mobile of the first kind is absolutely impossible.

2nd law: Exactly as the usual one [

(i) Particle at lower temperature (corresponding to small mass) cannot decay spontaneously into the one at higher temperature (corresponding to a large mass); while the constraints on the system and the state of the rest of the world are left unchanged (analogous to Clausius’).

(ii) It is impossible to find a single particle that produces no effect other than the transformation of its bound energy into an equivalent amount of useful form (analogous to Kelvin’s).

In other word, the particle perpetual mobile of the second kind never occurs. The important point is here that, if allow a particle transform its bound energy directly into the useful form, namely

2.5th law: In any particle process, the total momentum cannot increase, nor decrease, but remains constant. As a supplementary item, such law puts restrictions on which processes may occur, or more particularly which processes can never occur even though they are allowed by the 2nd. For example, the decay process of

3rd law: It is impossible to design a procedure that can control particle temperature to zero, namely, the absolute zero of particle is never attainable. This law disallows any decay process with 100% efficiency, even if for photon (with nonzero mass) [

To set up the state functions of a decay particle of mass width

can determine a mass distribution in the following form

Combing with the decay function of

Such the result can help us to write the adjusted enthalpy function in the form of

followed by the internal energy

So that, the total differential of the function reads

with the identifications:

Obviously,

Note that, the Maxwell relations for particle object are a consequence of the fact that the order of the cross derivatives of

accompanied with the chemical potential

These two are corresponding to the usual forms respectively

If further, apply Legendre transform to

including the variation of

The relationship enables us to explore an equilibrium criterion for an individual particle keeping contact with its surrounding bath

Now, consider a particle state with free energy

Variables | Internal energy | Enthalpy | Free energy | Free enthalpy | Temperature |
---|---|---|---|---|---|

TDS PO | |||||

Variables TDS PO | Entropy | Pressure | Volume | Chemical potential | Density |

where

Hence, to agree with Eq. (19) identifies

This is an analogue of Boltzmann relationship for particle physics, which can be made the basis of a theory of fluctuations about particle object in analogy to that of fluctuations about thermodynamic system. Specifically, the fluctuations in

where

Note the stable particle condition of

with a change ratio

equal to

Finally, by the definition of particle temperature, we can further get the following relation

with

Up to now, we have explored a new theory for the description of particle physics. And conceptually different from the conventional standpoint, this theory, by treating particle objects as a kind of thermodynamic system, has led to a number of apparently new results: (i) Particle decay behavior is restricted by Carnot’s theorem; (ii) There exist particle thermodynamic laws analogous to the usual ones. Especially, the momentum conservation principle is introduced to supplement the second law; (iii) Some thermodynamic functions, including an equilibrium criterion, are developed to describe particle states; (iv) Boltzmann relationship for particle physics is obtained. We here emphasize any microscopic particle in nature carries its intrinsic entropy with an absolute value near unit, and the total particle entropy never decreases for any decay process. It is important that we find a new route that can be followed to investigate particle physics in the mathematical framework of thermodynamics.

Qiankai Yao, (2015) Particle Physics Can Be Investigated from a Thermodynamic Point of View. Open Access Library Journal,02,1-8. doi: 10.4236/oalib.1101493