Lorentz covariant statistical mechanics and thermodynamics of the relativistic ideal gas and preferred frame

The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light), and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables a consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in the classical and quantum case.

Figure 1

The plot of the average energy $U$ per particle of the ideal gas of bradyons (dotted line), luxons (dashed line), and tachyons (solid line) given by Eqs. (3.10, 3.13, 3.14), respectively, where $u_0=1$, and $m=1$ in (3.10, 3.14), vs $kT$. The behavior of the average energy near the absolute zero.

Figure 2

The average energy $U$ per particle of the ideal gas of bradyons (dotted line), luxons (dashed line), and tachyons (solid line) given by Eqs. (3.10, 3.13, 3.14), respectively, where $u_0=1$, and $m=1$ in (3.10, 3.14), as a function of $kT$ on a logarithmic scale. The parameters $u_0$ and $m$ are the same as in Fig. 1.

Figure 3

The plot of the specific heat of the ideal gas of bradyons (dotted line), luxons (dashed line), and tachyons (solid line) given by (3.18, 3.19, 3.20), respectively, where $u_0=1$ and $k=1$, vs $T/m$.

Figure 4

A semilogarithmic graph in which the entropy per particle of the ideal gas of bradyons (dotted line), luxons (dashed line), and tachyons (solid line) given by Eqs. (3.27, 3.28, 3.29), respectively, where $u_0=1$, $k=1$, and $m=1$, are plotted against the temperature.

Figure 5

The plot of the function $f_b$ (dotted line), $f_l$ (dashed line), and $f_t$ (solid line) given by (3.37, 3.38, 3.39), related to the equation of state (3.36) for bradyons, luxons, and tachyons, respectively, where $u_0=1$, and $m=1$, in (3.37, 3.39), vs $kT$.

Figure 6

A semilogarithmic graph in which the squared velocity of particles of the ideal gas of bradyons given by (3.47), where $m=1$ is plotted against $kT$ on a logarithmic scale.

Figure 7

The average squared velocity of particles of the ideal gas of tachyons as a function of $kT$ (see (3.48)) on a logarithmic scale. The parameter $m$ is the same as in Fig. 6.