- The paper shows that imposing stationarity via equilibrium partition functions yields constraints on relativistic hydrodynamic transport coefficients derived from the second law of thermodynamics.
- It employs effective field theory methods on weakly curved backgrounds to recover known results for chiral fluids, including chiral magnetic and vorticity flows.
- The work suggests that aligning partition function constraints with second-order hydrodynamic expansions provides a promising avenue for addressing higher derivative corrections in gravitational theories.
Constraints on Fluid Dynamics from Equilibrium Partition Functions: A Summary
In the paper titled "Constraints on Fluid Dynamics from Equilibrium Partition Functions," the authors investigate the structural constraints imposed on relativistic hydrodynamics by requiring compatibility with equilibrium partition functions. Specifically, the analysis is conducted for quantum field theories on arbitrary stationary spacetimes with accompanying stationary background gauge fields. The authors aim to demonstrate that these constraints coincide with relations between hydrodynamic transport coefficients derived from the local form of the second law of thermodynamics.
The authors explore the thermal partition function in settings governed by the equations of relativistic hydrodynamics. They elucidate how these equations must correspond to a stationary solution on a weakly curved background manifold and generate conserved currents derivable from an equilibrium partition function. The research critically evaluates the hydrodynamic equations' consistency under these conditions, revealing that this requirement imposes both inequalities and equalities on transport coefficients related to parameters like viscosities and conductivities.
The core idea is that the relations between transport coefficients emanating from thermodynamic principles should align with constraints from the equilibrium partition function to all orders in the derivative expansion. The authors conjecture that this alignment is universally true, although a fuller investigation is suggested for future work.
The concept is applied through detailed examinations of several examples, including chiral fluids in 3+1 dimensions affected by anomalies. By analyzing the thermal partition function, the authors recover the known results for chiral magnetic and vorticity flows derived by Son and Surowka, addressing the chiral anomaly without resorting to entropy current considerations.
Importantly, this work highlights the potential utility of these results for understanding constraints on higher derivative corrections to Einstein's equations, reinforcing them through the fluid-gravity correspondence of the AdS/CFT duality. The authors elaborate on the effective field theory methods in the long-wavelength limit, introducing how equations of state can encapsulate arbitrary smooth background conditions. This is exemplified by their expanded partition function, which includes terms characterizing the fluid's response to electromagnetic anomalies.
Materially, the text demonstrates how these constraints manifest at the second order in derivative expansions for uncharged fluids and introduces the unique needs for parity-violating charged fluids in lower dimensions. The equilibrium analysis provides keen insights into possible corrections needed in second-order hydrodynamic expansions to maintain coherence with known thermodynamic principles.
The research opens up future discourse by calling attention to areas ripe for further exploration, such as the role of time dependence, higher derivative contributions, potential extensions to other classes of anomalies, and how these constraints intrinsically intertwine with the rich framework of general relativistic hydrodynamics.
Finally, the authors assert that the method described presents an innovative approach that is mathematically less formidable than traditional entropy-based methods, particularly when extended to non-parity-symmetric systems, offering a fresh perspective on longstanding issues within the domain of hydrodynamic equations and their derivations.