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to introduce a dimensionless dipolar interaction strength 

where n = N/ V is the number density of the system and ϵ 0 F = ℏ $^{2}$( k 0 $_{F}$) $^{2}$/ (2 m ) with k 0 F = (6 π $^{2}$n ) 1 / $^{3}$. We note that k 0 F and ϵ 0 F are, respectively, the Fermi wavevector and Fermi energy of an ideal Fermi gas. 

We plot the phase-space distribution function f ( k ) in Fig. 1 (a) and (b) for various temperatures and D$_{h}$ = 0 . 3. At low temperature, the momentum distri- bution is clearly stretched along z -axis. However, as one increases the temperature, the momentum distribution becomes less anisotropic. Such behavior can be most easily visualized by calculating the aspect ratio of the cloud in momentum space α ≡ √ 〈 k 2 $_{x}$〉 / 〈 k 2 $_{z}$〉 . Figure 1 (c) shows the temperature dependence of α correspond- ing to various dipolar interaction strengths. For small T , α approaches to the value at zero temperature; as one increases the temperature, α goes to unit asymptotically. 

Due to the spatial homogeneity of the system, the di- rect dipolar interaction energy vanishes. Therefore, the total energy only contains the contributions from kinetic energy and Fock exchange interaction. In Fig. 2 (a) and (b), we plot, respectively, E$_{kin}$ and E$_{exc}$ as functions of the temperature. The kinetic energy corresponding to stronger dipolar interaction is larger than that with weaker dipolar interaction, since the stronger dipolar in- teraction results in larger momentum space deformation. As to the exchange interaction energy, we see that E$_{exc}$ vanishes as α approaches 1 at high temperature limit. We 

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also plot the temperature dependence of the chemical po- tential in Fig. 2 (c). Clear ly, µ decreases as one increases T , in analogy to the ide al Fermi gas. In addition, the chemical potential is also a decreasing function of D$_{h}$ . This can be most easily u nderstood at zero temperature limit, where the chemical potential becomes [20] 

in weak interaction regim e ( D$_{h}$ ≪ 1). Equation (6) in- dicates that, for given de nsity n , the chemical potential decreases as the dipolar interaction strength grows. 

To calculate other ther modynamic quantities, we work with the thermodynamic potential 

where 

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is the entropy of the system. The pressure directly relates to the thermodynamics potential as P V = − Ω( T, V , µ ) and the heat capacity can also be evaluated using the definition C V = T ( ∂S ∂T ) V $_{N}$. In Fig. 3, we present the temperature dependence of P , S , and C V corresponding to different dipolar interaction strengths. As a compar- ison, we also plot the results for an ideal Fermi gas. In general, the results for dipolar Fermi gases approach to those corresponding to the ideal gas at high temperature limit. 

Figure 3 (a) also indicates that, at a given tempera- ture, P is a decreasing function of D$_{h}$ , in agreement with the zero temperature result [11]. This can be understood since the overall dipolar interaction is attractive for ho- mogeneous gas. In addition, even though S vanishes at zero temperature, the entropy for given T ̸ = 0 also ex- hibits a similar dependence on D$_{h}$ as the pressure [Fig. 3 (b)]. Furthermore, The temperature and interaction de- pendence of the heat capacity, shown in Fig. 3 (c), can be naturally deduced from the behavior of th entropy. 

To gain more insight into the entropy, we shall derive an analytical expression for S at low temperature limit. To this end, we note that when T → 0, the derivative of S with respect to T at constant V and µ can be approx- imately expressed as [21] 

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where we have explicitly expressed f as a function of the temperature T and the zero temperature dispersion relation for the quasi-particle is [12] 

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