Thermodynamics of Information Processing Massimiliano Esposito Honolulu, January 7, 2019 Outline ● Work principle in !tochastic Thermodynamics ● Work principle in #"emical Reaction Net&orks Homogeneous $eaction'(iffusion ● #onclusions 2 Stochastic Thermodynamics Master Equation may depend on time Local Detailed Balance th 0 law: at equilibrium * ,nergy. Entro y. 1st law Energy Balance Work Heat 2nd law Entropy Balance ,ntro y ,ntro y change change in the reser-oir ,ntro y production [Van den Broeck & Esposito, Physica A 418, 6 ( !"#$% + Landauer1s Principle y & r e n E Work 1/2 1/2 Heat 1 0 logic state 0 1 0 1 pf peq,i In finite time. accuracy'dissipation trade-offs [Diana, Ba&ci, Esposito, PRE 85, 0'"" # (2!" $% / Work Principle in& y pi ri) & d r m e riu n ilib pf E + qu n e n, o o i n + t n a o * i a t l a e * r a 1/2 1/2 1 0 l e r logic equilibrium dri)in& state 0 1 0 1 peq,i peq,f In general (com5ining 1st and 2nd la&6. nonequilibrium (ree energy: relative entropy: 3 [Esposito & Van den Broeck, EPL 95, '!!!' (2!""$% Nonequilibrium State as a Resource 0onequilibrium state in a &i)en energy landscape -ure waist: 0 0 x ! /ptimal e*traction: x 0 0 0 7 [Esposito & Van den Broeck, EPL 95, '!!!' (2!""$% (ynamics of Closed CRNs 1toichiometric matrix Environment Chemical Network k91 A + E E* k'1 k9+ k'2 k'+ k92 k'* E** E + B k9* Rate equations Reactions 4deal Dilute Solution + Elementary Reactions = Mass action kinetics 8 (ynamics of Open CRNs Environment Chemical Network k91 A + E E* k'1 Ae k9+ k'2 k'+ k92 k'* E** E + B Stoic2iometric matrix k9* Be Internal Chemosta8ed Rate equations In open nondriven 70 Reactions Exchange 9 Thermodynamics of CRNs Enthalpy of (ormation Entropy of formation Ideal Dilute Solutions Local equilibrium Standard-state chemical potential Local Detailed Balance 0th law of Thermodynamics: Closed 730 rela* to equilibrium detailed-balance 10 First and Second Law total 730 Enthalpy: 730 Entropy: concentration 72emical ;ork 1st law Enthalpy Balance 9eat :lo. 2nd law Entropy Balance Entropy chan&e in (thermal & c2emical$ reser)oirs Entropy production: 11 [3ao & Esposito, Phys. Rev. X 6, 0'"!64 ( !16$% Cost for manipulating Nonequilibrium States 7losed 730 0on,Eq< Gibbs (ree ener&y >Relative entropy? Relaxation to Eq: or Min .ork produced: Max .ork extracted: 12 [3ao & Esposito, Phys. Rev. X 6, 0'"!64 ( !16$% $eaction;(iffusion Reaction—Diffusion Equations Mass,action kinetics DiAusion: :ickBs La. Diffusion Reactions E*c2ange Diffusion coeAicients g n vi ri . d eq on n Spacial structuring takes work: iving eq. dr 1* [Falasco, Cao & Esposito, Phys. Rev. Lett. 121, 1!DE!" (2!"D$% Conclusions - Stochastic dynamics: multiple reser)oirs & conser)ation la.s [Cao & Esposito. New J. Phys. 20, 0 E!!F (2!"D$% , 1tochastic C30s [Cao & Esposito, JCP 149 , '#"!" (2!"D$% 1+.