Gibbs state in quantum statistical physics

Yuri Suhov

Ola Bratteli, Derek W. Robinson

Anton Sergeevich Trushechkin, Marco Merkli, James D. Cresser +1 more

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and energies of the system. However, at decreasing system sizes, i.e., for nanoscale and quantum systems, the interaction with their environments is not negligible. The question then arises: Is the system's steady state still the Gibbs state? If not, how may the steady state depend on the interaction details? Here, we provide an overview of recent progress on answering these questions. We expand on the state of the art along two general avenues: First, we take the static point-of-view, which postulates the so-called mean force Gibbs state. This view is commonly adopted in the field of strong coupling thermodynamics, where modified laws of thermodynamics and nonequilibrium fluctuation relations are established on the basis of this modified state. Second, we take the dynamical point of view, originating from the field of open quantum systems, which examines the time-asymptotic steady state within two paradigms. We describe the mathematical paradigm, which proves return to equilibrium, i.e., convergence to the mean force Gibbs state, and then discuss a number of microscopic physical methods, particularly master equations. We conclude with a summary of established links between statics and equilibration dynamics and provide an extensive list of open problems. This comprehensive overview will be of interest to researchers in the wider fields of quantum thermodynamics, open quantum systems, mesoscopic physics, statistical physics, and quantum optics and will find applications whenever energy is exchanged on the nanoscale, from quantum chemistry and biology to magnetism and nanoscale heat management.

Sophia E. Economou, Ada Warren, Edwin Barnes

Sampling from distributions is an important capability for a range of tasks in science and engineering, including in machine learning applications. Quantum computers hold promise for the capability of sampling from distributions that are hard to sample from with usual (classical) computers. We have recently introduced an adaptive quantum variational algorithm for Gibbs state preparation, a state that can be sampled to yield a thermal (or Gibbs) distribution. This has applications in statistical physics, stochastic processes, and optimization. Here we explore the role of the initial quantum correlations (i.e., entanglement) built into the ‘data’ quantum bits (those that will be sampled) and the ancilla quantum bits (those that assist in preparing the Gibbs state) in the run-time of the adaptive state-preparation algorithm. Based on our simulations, we conclude that certain types of entangled states perform better for Ising Hamiltonians, while others are more appropriate for XY Hamiltonians. We also show that both perform well if multiple operators are added at each iteration through the ‘TETRIS-ADAPT’ technique.

Vittorio Gorini, Alberto Frigerio, Maurizio Verri

Anharmonic Oscillators, Yuri V. Kozitsky