Work relations with measurement and feedback control on nonuniform temperature systems

Abstract

The relation between the work performed to a system and the change of its free energy during a certain process is important in nonequilibrium statistical mechanics. In particular, the work relation with measurement and feedback control has attracted much attention, because it resolved the paradox concerning Maxwell's demon. Most studies, however, assume that their target systems are isolated or isothermal. In this paper, by considering a nonisothermal system, we generalize the Sagawa-Ueda-Jarzynski relation, which involves measurement and feedback control, and apply it to a realistic model. Furthermore, when the temperature profile is quadratic, we see that the system is governed by Tsallis statistical mechanics. In addition, we show that our formulation provides the generalized version of the second law of information thermodynamics and a set of new work relations for isothermal systems.

Thermodynamics of Quantum Information Flows

“…For a large class of systems [4][5][6] 9] the entropy production can be defined as σ ≡ ∆S − α Q α β α , where ∆S is the change of the Shannon or the von Neumann entropy of the system (which is well defined also out of equilibrium) and Q α is the heat delivered to the system from the reservoir α with the inverse temperature β α ; additionally, in Markovian systems the entropy production rateσ is always nonnegative [7, 10]. Formulations generalizing the free energy inequality [11][12][13][14] are much less common and have been so far confined mainly to systems coupled to an environment with a homogeneous temperature; for an exception, see Ref. [14].These developments have also brought a deeper understanding of the relation between thermodynamics and the information theory [12,15].…”

“…Formulations generalizing the free energy inequality [11][12][13][14] are much less common and have been so far confined mainly to systems coupled to an environment with a homogeneous temperature; for an exception, see Ref. [14].These developments have also brought a deeper understanding of the relation between thermodynamics and the information theory [12,15]. One of the most important achievements is related to the field of thermodynamics of feedback-controlled systems [16].…”

“…Formulations generalizing the free energy inequality [11][12][13][14] are much less common and have been so far confined mainly to systems coupled to an environment with a homogeneous temperature; for an exception, see Ref. [14].…”

Nonequilibrium free energy and information flow of a double quantum-dot system with Coulomb coupling

“…Esposito introduced the concept of nonequilibrium system free energy to understand the irreversible work in Hamiltonian dynamics of an open driven system [21,22]. More recently, the investigations of free energy were generalized to the systems coupled to the environment with multiple heat baths [23][24][25][26]. More and More studies utilized the nonequilibrium Clausius and free energy inequalities to clarify the information and energy regimes in the nonequilibrium systems [27][28][29][30][31][32][33][34][35].…”

“…More and More studies utilized the nonequilibrium Clausius and free energy inequalities to clarify the information and energy regimes in the nonequilibrium systems [27][28][29][30][31][32][33][34][35]. Miyahara et al derived the Sagawa-Ueda-Jarzynski relation under a nonisothermal system to measure the change of the free energy [26]. Ptaszyński et al formulated a nonequilibrium free energy inequality for a generic open quantum system weakly coupled to multi heat sources [23].…”