Conservation Laws in Nonequilibrium Thermodynamics: Stochastic Processes, Chemical Reaction Networks, and Information Processing

Doctoral thesis (2018)

Thermodynamics has a long history. It was established during the 19th century as a phenomenological theory grasping the principles underlying heat engines. In the 20th and 21st centuries its range of ... [more ▼]

Thermodynamics has a long history. It was established during the 19th century as a phenomenological theory grasping the principles underlying heat engines. In the 20th and 21st centuries its range of applicability was extended to nonequilibrium stochastic and chemical processes. However a systematic procedure to identify the thermodynamic forces at work in these systems was lacking. In this thesis, we provide one by making use of conservation laws. Of particular importance are the conservation laws which are broken when putting the system in contact with different reservoirs (thermostats or chemostats). These laws depend on the internal structure of the system and are specific to each system. We introduce a systematic procedure to identify them and show how they shape the entropy production (i.e. the dissipation) into fundamental contributions. Each of these provides precious insight on how to drive and control the system out of equilibrium. We first present our results at the level of phenomenological thermodynamics. We then show that they can be systematically derived for various dynamics: Markov jump processes used in stochastic thermodynamics, also including the chemical master equation, and deterministic chemical rate equations with and without diffusion, which are used to describe chemical reaction networks. Generalized nonequilibrium Landauer principles ensue form our theory. They predict that the minimal thermodynamic cost necessary to transform the system from an arbitrary nonequilibrium state to another can be expressed in terms of information metrics such as relative entropies between the equilibrium and nonequilibrium states of the system. [less ▲]

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

in New Journal of Physics (2018), 20(4), 042002

Starting from the detailed catalytic mechanism of a biocatalyst we provide a coarse-graining procedure which, by construction, is thermodynamically consistent. This procedure provides stoichiometries ... [more ▼]

Starting from the detailed catalytic mechanism of a biocatalyst we provide a coarse-graining procedure which, by construction, is thermodynamically consistent. This procedure provides stoichiometries, reaction fluxes (rate laws), and reaction forces (Gibbs energies of reaction) for the coarse-grained level. It can treat active transporters and molecular machines, and thus extends the applicability of ideas that originated in enzyme kinetics. Our results lay the foundations for systematic studies of the thermodynamics of large-scale biochemical reaction networks. Moreover, we identify the conditions under which a relation between one-way fluxes and forces holds at the coarse-grained level as it holds at the detailed level. In doing so, we clarify the speculations and broad claims made in the literature about such a general flux–force relation. As a further consequence we show that, in contrast to common belief, the second law of thermodynamics does not require the currents and the forces of biochemical reaction networks to be always aligned. [less ▲]

Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics

in Physical Review X (2016), 6(4), 041064

We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of <br /><br />elementary reactions. Their dynamics is described by deterministic rate equations with mass ... [more ▼]

We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of <br /><br />elementary reactions. Their dynamics is described by deterministic rate equations with mass action <br /><br />kinetics. Our most general framework considers open networks driven by time-dependent chemostats. <br /><br />The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced. <br /><br />The difference between this latter and its equilibrium form represents the minimal work done by the <br /><br />chemostats to bring the network to its nonequilibrium state. It is minimized in nondriven detailed-balanced <br /><br />networks (i.e., networks that relax to equilibrium states) and has an interesting information-theoretic <br /><br />interpretation. We further show that the entropy production of complex-balanced networks (i.e., networks <br /><br />that relax to special kinds of nonequilibrium steady states) splits into two non-negative contributions: one <br /><br />characterizing the dissipation of the nonequilibrium steady state and the other the transients due to <br /><br />relaxation and driving. Our theory lays the path to study time-dependent energy and information <br /><br />transduction in biochemical networks. [less ▲]

Thermodynamics of accuracy in kinetic proofreading: dissipation and efficiency trade-offs

in Journal of Statistical Mechanics: Theory and Experiment (2015)

The high accuracy exhibited by biological information transcription processes is due to kinetic proofreading, i.e. by a mechanism which reduces the error rate of the information-handling process by ... [more ▼]

The high accuracy exhibited by biological information transcription processes is due to kinetic proofreading, i.e. by a mechanism which reduces the error rate of the information-handling process by driving it out of equilibrium. We provide a consistent thermodynamic description of enzyme-assisted assembly processes involving competing substrates, in a master equation framework. We introduce and evaluate a measure of the efficiency based on rigorous non- equilibrium inequalities. The performance of several proofreading models are thus analyzed and the related time, dissipation and efficiency versus error trade-offs exhibited for different discrimination regimes. We finally introduce and analyse in the same framework a simple model which takes into account correlations between consecutive enzyme-assisted assembly steps. This work highlights the relevance of the distinction between energetic and kinetic discrimination regimes in enzyme-substrate interactions. [less ▲]