May 27, 2020—May 29, 2020

Stochastic thermodynamics is an emerging 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 which satisfies local detailed balance, 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 — this is especially the case with correlated, path-dependent and driven systems. 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.

This raises a host of 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) In conventional stochastic thermodynamics physics, typically we are allowed to vary the trajectory of the Hamiltonian through time in arbitrary ways. But in the real world we never have such freedom. A simple example of such a constraint on the allowed trajectory of Hamiltonians is the scenario mentioned in (1), in which there is a finite heat bath – one way to formalize such a scenario is by decomposing the system into two subsystems, one of which we identify as the “finite heat bath”, and to only allow ourselves to vary the Hamiltonian over the other subsystem. What are the thermodynamic consequences of constraints on the kinds of dynamic changes we can make to the Hamiltonian of the system? How do the answers depend on associated constraints on the rate matrix of the Markov process? What if the system is non-Markovian? How does the answer change if there is no external (infinite) heat reservoir coupled to the system?