Landau theory for finite-time dynamical phase transitions

Abstract

We study the time evolution of thermodynamic observables that characterise the dissipative nature of thermal relaxation after an instantaneous temperature quench. Combining tools from stochastic thermodynamics and large-deviation theory, we develop a powerful theory for computing the large-deviation statistics of such observables. Our method naturally leads to a description in terms of a dynamical Landau theory, a versatile tool for the analysis of finite-time dynamical phase transitions. The topology of the associated Landau potential allows for an unambiguous identification of the dynamical order parameter and of the phase diagram. As an immediate application of our method, we show that the probability distribution of the heat exchanged between a mean-field spin model and the environment exhibits a singular point, a kink, caused by a finite-time dynamical phase transition. Using our Landau theory, we conduct a detailed study of the phase transition. Although the manifestation of the new transition is similar to that of a previously found finite-time transition in the magnetisation, the properties and the dynamical origins of the two turn out to be very different.

30 pages, 9 figures

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Cited by in corpus (15)

• Macroscopic Stochastic Thermodynamics
• Discontinuous phase transition from ferromagnetic to oscillating states in a nonequilibrium mean-field spin model
• Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways
• Critical heat current fluctuations in Curie-Weiss model in and out of equilibrium
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Critical Fluctuations at Finite-Time Dynamical Phase Transition
• Nonequilibrium fluctuation-response relations for state observables
• Nonequilibrium fluctuation-response relations for state-current correlations
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• Fluctuation corrections to Lifshitz tails in disordered systems
• Exponential Change of Relaxation Rate by Quenched Disorder
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Full distribution of the ground-state energy of potentials with weak disorder
• Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference