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

TL;DR

This paper introduces a strengthened second law of thermodynamics for multi-dimensional systems with multiple reservoirs, incorporating constraints on subsystem interactions, applicable to complex systems like biological or economic systems.

Contribution

It extends the second law to complex, multi-dimensional systems with constraints, even when subsystems change states simultaneously, without requiring local detailed balance.

Findings

Strengthened second law applies to complex systems with subsystem constraints.

Bounds on work extraction are improved for multi-dimensional systems.

Applicable to biological, economic, and other complex systems.

Abstract

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 \textit{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.