The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped one-dimensional systems. Despite this fact, its complete thermodynamic description in all its regimes has been lacking. Here, we fill this gap and derive the framework that captures its thermodynamics and serves as the basis of its hydrodynamic description. As a first application, we compute the Drude weight characterizing the ballistic transport of topological charge and demonstrate that its dependence on the value of the coupling shows a fractal structure, similar to the gapless phase of the XXZ spin chain. The thermodynamic framework can be applied to study other features of nonequilibrium dynamics in the sine-Gordon model using generalized hydrodynamics, opening the way to a wide array of theoretical studies and potential novel experimental predictions.

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• Ballistic transport
• Lower-dimensional field theories
• Statistical field theory
• Strongly correlated systems
• Bethe ansatz
• Integrable systems