A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early universe and in particle colliders, starting from the Standard Model. Classical-computing methods, via the framework of lattice gauge theory, have experienced limited success in this mission. Quantum simulation of lattice gauge theories holds promise for overcoming computational limitations. Because of local constraints (Gauss’s laws), lattice gauge theories have an intricate Hilbert-space structure. This structure complicates the definition of thermodynamic properties of systems coupled to reservoirs during equilibrium and nonequilibrium processes. We show how to define thermodynamic quantities such as work and heat using strong-coupling thermodynamics, a framework that has recently burgeoned within the field of quantum thermodynamics. Our definitions suit instantaneous quenches, simple nonequilibrium processes undertaken in quantum simulators. To illustrate our framework, we compute the work and heat exchanged during a quench in a $Z_2$ lattice gauge theory coupled to matter in 1+1 dimensions. The thermodynamic quantities, as functions of the quench parameter, evidence an expected phase transition. Generally, we derive a simple relation between a quantum many-body system’s entanglement Hamiltonian, measurable with quantum-information-processing tools, and the Hamiltonian of mean force, used to define strong-coupling thermodynamic quantities.

*This work was supported in part by the National Science Foundation (NSF) Quantum Leap Challenge Institutes (QLCI) (award no. OMA-2120757), by the Department of Energy (DOE), Office of Science, Early Career Award (award no. DESC0020271), and by the Department of Physics, Maryland Center for Fundamental Physics, and the College of Computer, Mathematical, and Natural Sciences at the University of Maryland, College Park, and the Simons Foundation through the Simons Foundation Emmy Noether Fellows Program at Perimeter Institute, by the John Templeton Foundation (award no. 62422), and by the DOE, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (award no. DE-SC0020970). *