Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs

The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of a priori constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly, the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.

[1]  D. Wolpert.  Combining lower bounds on entropy production in complex systems with multiple interacting components , 2022, 2208.02902.

[2]  S. Klapp,et al.  Irreversibility, heat and information flows induced by non-reciprocal interactions , 2020, New Journal of Physics.

[3]  D. Wolpert.  Minimal entropy production rate of interacting systems , 2020, New Journal of Physics.

[4]  D. M. Busiello,et al.  Thermodynamic bound on speed limit in systems with unidirectional transitions and a tighter bound , 2020, 2009.11115.

[5]  M. Esposito,et al.  Dissipation-Time Uncertainty Relation. , 2020, Physical review letters.

[6]  D. Wolpert,et al.  Entropy production and thermodynamics of information under protocol constraints , 2020, ArXiv.

[7]  Van Tuan Vo,et al.  Unified approach to classical speed limit and thermodynamic uncertainty relation. , 2020, Physical review. E.

[8]  A. Maritan,et al.  Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems , 2020 .

[9]  U. Seifert,et al.  Thermodynamic Uncertainty Relation for Time-Dependent Driving. , 2020, Physical review letters.

[10]  D. Wolpert.  Fluctuation theorems for multipartite processes , 2020, 2003.11144.

[11]  Todd R. Gingrich,et al.  Thermodynamic uncertainty relations constrain non-equilibrium fluctuations , 2020, Nature Physics.

[12]  Masahito Ueda,et al.  Thermodynamic Uncertainty Relation for Arbitrary Initial States. , 2019, Physical review letters.

[13]  D. Wolpert.  Uncertainty relations and fluctuation theorems for Bayes nets , 2019, Physical review letters.

[14]  M. Esposito,et al.  Unifying thermodynamic uncertainty relations , 2019, New Journal of Physics.

[15]  R. Ch'etrite,et al.  Information thermodynamics for interacting stochastic systems without bipartite structure , 2019, Journal of Statistical Mechanics: Theory and Experiment.

[16]  David H. Wolpert,et al.  The stochastic thermodynamics of computation , 2019, Journal of Physics A: Mathematical and Theoretical.

[17]  Yunxin Zhang.  Comment on "Speed Limit for Classical Stochastic Processes" , 2018, 1811.06978.

[18]  M. N. Bera,et al.  Thermodynamics from Information , 2018, 1805.10282.

[19]  K. Funo,et al.  Speed Limit for Classical Stochastic Processes. , 2018, Physical review letters.

[20]  M. Ohzeki,et al.  Quantum Speed Limit is Not Quantum. , 2017, Physical review letters.

[21]  Todd R. Gingrich,et al.  Proof of the finite-time thermodynamic uncertainty relation for steady-state currents. , 2017, Physical review. E.

[22]  Todd R. Gingrich,et al.  Fundamental Bounds on First Passage Time Fluctuations for Currents. , 2017, Physical review letters.

[23]  M. Esposito,et al.  Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining. , 2017, Physical review. E.

[24]  Thomas E. Ouldridge,et al.  What we learn from the learning rate , 2017, 1702.06041.

[25]  Frank Julicher,et al.  Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes , 2016, 1604.04159.

[26]  Adam Lipowski,et al.  Phase transitions in Ising models on directed networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Udo Seifert,et al.  Sensory capacity: An information theoretical measure of the performance of a sensor. , 2015, Physical review. E.

[28]  Heinrich Meyr,et al.  Decision Making in the Arrow of Time. , 2015, Physical review letters.

[29]  T. Sagawa,et al.  Thermodynamics of information , 2015, Nature Physics.

[30]  J. Horowitz.  Multipartite information flow for multiple Maxwell demons , 2015, 1501.05549.

[31]  Udo Seifert,et al.  Stochastic thermodynamics with information reservoirs. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Takahiro Sagawa,et al.  Fluctuation theorem for partially masked nonequilibrium dynamics. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Massimiliano Esposito,et al.  Ensemble and trajectory thermodynamics: A brief introduction , 2014, 1403.1777.

[34]  C. Broeck,et al.  Work statistics in stochastically driven systems , 2014, 1402.5777.

[35]  Jordan M. Horowitz,et al.  Thermodynamics with Continuous Information Flow , 2014, 1402.3276.

[36]  A. C. Barato,et al.  Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a Maxwell’s demon interpretation , 2014, 1402.0419.

[37]  U. Seifert.  Stochastic thermodynamics, fluctuation theorems and molecular machines , 2012, Reports on progress in physics. Physical Society.

[38]  Masahito Ueda,et al.  Nonequilibrium thermodynamics of feedback control. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  A. P. Beltyukov,et al.  On the amount of information , 2011, Pattern Recognition and Image Analysis.

[40]  Masahito Ueda,et al.  Generalized Jarzynski equality under nonequilibrium feedback control. , 2009, Physical review letters.

[41]  H. Hasegawa,et al.  Generalization of the Second Law for a Nonequilibrium Initial State , 2009, 0907.1569.

[42]  Masahito Ueda,et al.  Minimal energy cost for thermodynamic information processing: measurement and information erasure. , 2008, Physical review letters.

[43]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[44]  Juan M. López,et al.  Nonequilibrium phase transitions in directed small-world networks. , 2001, Physical review letters.

[45]  C. Jarzynski.  Hamiltonian Derivation of a Detailed Fluctuation Theorem , 1999, cond-mat/9908286.

[46]  P. Goldman.  Comment I , 1975 .

[47]  W. J. McGill.  Multivariate information transmission , 1954, Trans. IRE Prof. Group Inf. Theory.

[48]  D. Wolpert,et al.  Thermodynamic speed limits for multiple, co-evolving systems , 2021 .

[49]  I. Neri.  Dissipation bounds the moments of first-passage times of dissipative currents in nonequilibrium stationary states , 2021 .

[50]  Hu Kuo Ting,et al.  On the Amount of Information , 1962 .

[51]  Statistical Mechanics: J Theory and Thermodynamic limits to information harvesting by sensory systems , 2022 .