Scaling law for irreversible entropy production in critical
Scaling law for irreversible entropy production in critical systems Junghyo Jo (APCTP) (Workshop on stochasticity and fluctuations in small systems, Dec. 2, 2016)
Fluctuation theorem S 1 S 2 T T § Equality relation for nonequilibrium processes (Jarzynski, 1997) (Crooks, 1999) § Information thermodynamics
Convergence problem (Zuckerman & Woolf, 2002; Gore, Ritort & Bustamante, 2003; Jarzynski, 2006)
Absolute irreversibility Forward T Backward T T (Lua & Grosbert, 2005; Sung, 2005; Gross, 2005; Jarzynski, 2005; Horowitz & Vaikuntanathan, 2010; Murashita, Funo & Ueda, 2014)
Phase transition Spontaneous symmetry breaking “Absolute irreversibility & finite sampling issues can take place in a single setup at criticality. ” Gentaro Watanabe (Zhejiang U) Finite size effect
Quenching of Ising model
Sudden quenching
Jarzynski equality under sudden quenching
Jarzynski equality under sudden quenching
Tolerance parameter
Empty symbol: δ=0. 1 Filled symbol: δ=0. 3 Monte-Carlo results L=50 L=100 L=20 L=40 L=50
Scaling law “Hmm… I may explain the scaling behavior. ” Mahn-Soo Choi (Korea U) Relative separation
Scaling law Critical exponents Universal scaling functions Rushbrooke scaling law Joshephson hyperscaling law (d<d*)
Empty symbol: δ=0. 1 Filled symbol: δ=0. 3 Monte-Carlo results L=50 L=100 L=20 L=40 L=50
Scientific Reports 6: 27603 (2016) § Fluctuation theorem can be used to obtain equilibrium free energy. § Fluctuation theorem can be used to explore critical phenomena.
Configuration vs. magnitization Magnetization (order parameter) Spin configuration Energy
Finite speed quenching Kibble-Zurek mechanism Adiabatic regime: No entropy production given sufficient relaxation time Impulse regime: Sudden quenching given slow relaxation (frozen configuration)
- Slides: 17
