0 1 2 P V / ( Nϵ 0 F ) (a) 0 1 2 3 S/ ( Nk B ) (b) 0 0.5 1 1.5 2 0.5 1 1.5 k$_{B}$T/ϵ 0 F C V / ( Nk B ) (c) FIG. 3: (Color online). The temperature dependence of the pressure (a), entropy (b), and heat capacity (c). The dimen- sionless dipolar interaction strength are D$_{h}$ = 0 (dash-dotted lines), 0 . 2 (dashed lines), and 0 . 3 (solid lines). D$_{h}$ = nc$_{d}$ ϵ 0 F , Ω( T, V , µ ) = E − T S − µN, (7) µ$_{0}$ ϵ 0 F ≃ ( 1 − 8 π 2 15 D 2 h ) 2 / 3 (6) S V k$_{B}$ = − ∫ d k (2 π ) 3 { f ( k ) ln f ( k ) + [1 − f ( k )] ln[1 − f ( k )] } . T ( ∂S ∂T ) V µ = V ∫ d k (2 π ) 3 ( ε$_{0}$ ( k ) − µ ) ∂f ( k , T ) ∂T , ε$_{0}$ ( k ) ≃ ℏ $^{2}$k2 2 m − 2 ϵ 0 $_{F}$D$_{h}$ P$_{2}$ (cos θ ) I ( k k 0 F ) , 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 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 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] 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] 3