2017/01/31 by Ping Gao, Hong Liu · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #BRST quantization #Classical mechanics #Degrees of freedom (physics and chemistry) #Dynamical systems theory #Gauge theory #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Path integral formulation #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Statistical physics #Supersymmetry #Symmetry (geometry) #Theoretical and Computational Physics #Theoretical physics #Thermal equilibrium #Unitarity #cond-mat.stat-mech #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep01(2018)040
45 pages
arxiv created 2017/09/22 · openalex publication_date 2018/01/01 · arxiv updated 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Many physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and can be considered as in local thermal equilibrium. In this paper we show that any classical statistical system in local thermal equilibrium has an emergent supersymmetry at low energies. We use the framework of non-equilibrium effective field theory for quantum many-body systems defined on a closed time path contour and consider its classical limit. Unitarity of time evolution requires introducing anti-commuting degrees of freedom and BRST symmetry which survive in the classical limit. The local equilibrium is realized through a Z2 dynamical KMS symmetry. We show that supersymmetry is equivalent to the combination of BRST and a specific consequence of the dynamical KMS symmetry, to which we refer as the special dynamical KMS condition. In particular, we prove a theorem stating that a system satisfying the special dynamical KMS condition is always supersymmetrizable. We discuss a number of examples explicitly, including model A for dynamical critical phenomena, a hydrodynamic theory of nonlinear diffusion, and fluctuating hydrodynamics for relativistic charged fluids.