#### This workshop is organized by David Wolpert, Santa Fe Institute & CSH External Faculty and Jan Korbel, CSH Associate Faculty.

#### Due to the coronavirus pandemic, we will do it as a video conference. If you are interested in participating, please email to office@csh.ac.at.

Please find the workshop agenda HERE.

Find below the schedule with links to some of the presentations.

#### Abstract

Stochastic thermodynamics is a powerful extension of conventional equilibrium statistical physics designed for analyzing non-equilibrium thermodynamics of small systems, down to the level of individual trajectories. In stochastic thermodynamics, we typically consider a system undergoing a continuous-time Markov process while coupled to (one or more) infinite heat, particle, or work reservoirs. If there is a single infinite heat reservoir and local detailed balance holds, then the equilibrium distribution is the ordinary Boltzmann distribution.

On the other hand, in many complex systems, the equilibrium distribution is different from the Boltzmann distribution. These kinds of equilibria arise because the reservoirs are finite, the dynamics are non-Markovian, or some other assumption of conventional stochastic thermodynamics is violated.

In addition, in conventional stochastic thermodynamics we are typically allowed to vary the trajectory of the Hamiltonian and rate matrices through time in arbitrary ways (perhaps subject to restrictions like local detailed balance, or irreducibility). But real-world systems are almost always extremely constrained in the kinds of trajectories of Hamiltonians and rate matrices they can follow. A simple example is if we decompose a closed system into two subsystems, one of which we identify as the “finite heat bath”, and then only allow ourselves to vary the Hamiltonian over the other subsystem. Another example is a system that is open, being connected to an infinite external heat bath, but which decomposes into a set of multiple subsystems, where there are locality-based constraints on which subsystem can directly affect which other subsystem.

These issues raise a host of intertwined questions, which this workshop aims to investigate:

1) What are the necessary and sufficient conditions for a thermodynamic system to have a non-Boltzmann equilibrium distribution, e.g., by having finite heat baths or an infinite number of baths? What equilibria arise if we extend conventional stochastic thermodynamics, e.g., to involve non-linear master equations (or in some other way violate the assumption of Markovian evolution)? How can we experimentally test such extensions of conventional stochastic thermodynamics? In particular, how can we identify experimentally accessible macroscopic quantities like thermodynamic work and heat with the quantities arising in such extensions of stochastic thermodynamic? Do we need to generalize the concept of entropy to analyze these scenarios? What is the role of Maximum entropy principle in these scenarios?

2) What are the thermodynamic consequences of constraints on the trajectories of the Hamiltonian and / or rate matrices? What if the system is non-Markovian? How does the answer change if there is no external (infinite) heat reservoir coupled to the system? Are there high-level taxonomies of the form of the constraints, which are useful for analyzing their thermodynamics behavior?