Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems

Abstract

Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical structure of an effective potential of a Hamiltonian, recovered from the macroscopic fluctuation theory description. Using this method we identify new dynamical phase transitions that could not be recovered using existing perturbative methods. Moreover, using the Hamiltonian picture, an experimental scheme is suggested to demonstrate an analog of dynamical phase transitions in linear, rather than exponential, time.

arXiv comment9 pages, 5 figures

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• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Large-time asymptotic of heavy tailed renewal processes
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions