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

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.