Nonequilibrium steady states of driven systems

5 problems

• When the additivity principle fails for current fluctuations

  Partially resolved

  Large current fluctuations in a driven conductor can be computed from a principle that assumes the most likely fluctuation keeps a fixed density profile in time. For some systems and currents the most likely fluctuation instead changes its profile in time or breaks a symmetry of the system, which is a phase transition in the fluctuations.

• Universal exponent of anomalous heat conduction in one dimension

  Contested

  In one-dimensional chains that conserve momentum, heat conductivity grows with chain length instead of staying fixed. Theory predicts universal growth exponents, but simulations of different chains disagree.

• A variational principle for stationary distributions of driven Markov processes

  Open

  In equilibrium, the Boltzmann distribution gives the probability of every state from its energy alone. For small driven systems that hop between states, no equivalent rule is known, and proposed rules such as minimum entropy production work only for weak driving.

• Existence of a thermodynamics for macroscopic driven steady states

  Contested

  Equilibrium thermodynamics predicts what happens when systems are put in contact or split into phases using a few numbers such as temperature and chemical potential. Whether driven macroscopic systems have a similar small set of numbers with the same predictive power is unknown.

• Zeroth law for two driven systems in weak contact

  Contested

  Two systems in equilibrium that exchange particles stop exchanging on average when their chemical potentials are equal. The question is whether driven systems have a similar quantity that equalizes on contact, independent of how they touch.